{"id":37573,"date":"2022-04-01T09:54:36","date_gmt":"2022-04-01T04:24:36","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=37573"},"modified":"2022-04-07T11:40:38","modified_gmt":"2022-04-07T06:10:38","slug":"big-ideas-math-algebra-1-answers-chapter-6","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers-chapter-6\/","title":{"rendered":"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences"},"content":{"rendered":"<p>Dreamt to become Pro in Math then having a good grip on <strong>Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences<\/strong> is mandatory. It is the ultimate guide for all high school students as it covers study resources for the concepts of chapter 6 Exponential Functions and Sequences. So, students can trust this bigideasmathanswers.com BIM Algebra 1 Solution Key and make it a part of their preparation. Practice &amp; solve the questions covered in the available Topic-wise BigIdeas Math Book Algebra 1 Ch 6 Answers PDF and identify the knowledge gap accordingly.<\/p>\n<h2 class=\"entry-title\">Big Ideas Math Book Algebra 1 Solution Key Chapter 6 Exponential Functions and Sequences<\/h2>\n<p>Make use of this provided Big Ideas Math Book Algebra 1 Ch 6 Exponential Functions and Sequences Answer Key topic-wise and clear all your subject doubts within seconds. <strong>BIM Algebra 1 Textbook Solutions for Chapter 6 Exponential Functions and Sequences<\/strong> concepts are explained in a step-wise manner so they are easy to understand while preparation. Also, BIM Answer Key for Algebra 1 Ch 6 is free to access online and offline at any time. Kickstart your preparation with the ultimate Ch 6 Exponential Functions and Sequences <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers\/\">Big Ideas Math Algebra 1 Answers<\/a> guide &amp; score highest marks in various exams.<\/p>\n<ul>\n<li><a href=\"#Exponential_Functions_and_Sequences_Maintaining_Mathematical_Proficiency\">Exponential Functions and Sequences Maintaining Mathematical Proficiency &#8211; Page 289\u00a0<\/a><\/li>\n<li><a href=\"#Exponential_Functions_and_Sequences_Mathematical_Practices\">Exponential Functions and Sequences Mathematical Practices &#8211; Page 290<\/a><\/li>\n<li><a href=\"#Lesson_6.1_Properties_of_Exponents\">Lesson 6.1 Properties of Exponents &#8211; Page(291-298)\u00a0<\/a><\/li>\n<li><a href=\"#Properties_of_Exponents_6.1_Exercises\">Properties of Exponents 6.1 Exercises &#8211; Page(296-298)<\/a><\/li>\n<li><a href=\"#Lesson_6.2_Radicals_and_Rational_Exponents\">Lesson 6.2 Radicals and Rational Exponents &#8211; Page(299-304)<\/a><\/li>\n<li><a href=\"#Radicals_and_Rational_Exponents_6.2_Exercises\">Radicals and Rational Exponents 6.2 Exercises &#8211; Page(303-304)<\/a><\/li>\n<li><a href=\"#Lesson_6.3_Exponential_Functions\">Lesson 6.3 Exponential Functions &#8211; Page(305-312)<\/a><\/li>\n<li><a href=\"#Exponential_Functions_6.3_Exercises\">Exponential Functions 6.3 Exercises &#8211; Page(310-312)<\/a><\/li>\n<li><a href=\"#Lesson_6.4_Exponential_Growth_and_Decay\">Lesson 6.4 Exponential Growth and Decay &#8211; Page(313-322)<\/a><\/li>\n<li><a href=\"#Exponential_Growth_and_Decay_6.4_Exercises\">Exponential Growth and Decay 6.4 Exercises &#8211; Page(319-322)<\/a><\/li>\n<li><a href=\"#Exponential_Functions_and_Sequences_Study_Skills:_Analyzing_Your_Errors\">Exponential Functions and Sequences Study Skills: Analyzing Your Errors &#8211; Page 323<\/a><\/li>\n<li><a href=\"#Exponential_Functions_6.1_-_6.4_Quiz\">Exponential Functions 6.1 &#8211; 6.4 Quiz &#8211; Page 324<\/a><\/li>\n<li><a href=\"#Lesson_6.5_Solving_Exponential_Functions\">Lesson 6.5 Solving Exponential Functions &#8211; Page(325-330)<\/a><\/li>\n<li><a href=\"#Solving_Exponential_Functions_6.5_Exercises\">Solving Exponential Functions 6.5 Exercises &#8211; Page(329-330)<\/a><\/li>\n<li><a href=\"#Lesson_6.6_Geometric_Sequences\">Lesson 6.6 Geometric Sequences &#8211; Page(331-338)<\/a><\/li>\n<li><a href=\"#Geometric_Sequences_6.6_Exercises\">Geometric Sequences 6.6 Exercises &#8211; Page(336-338)<\/a><\/li>\n<li><a href=\"#Lesson_6.7_Recursively_Defined_Sequences\">Lesson 6.7 Recursively Defined Sequences &#8211; Page(339-346)<\/a><\/li>\n<li><a href=\"#Recursively_Defined_Sequences_6.7_Exercises\">Recursively Defined Sequences 6.7 Exercises &#8211; Page(344-346)<\/a><\/li>\n<li><a href=\"#Exponential_Functions_and_Sequences_Performance_Task:_The_New_Car\">Exponential Functions and Sequences Performance Task: The New Car &#8211; Page 347<\/a><\/li>\n<li><a href=\"#Exponential_Functions_and_Sequences_Chapter_Review\">Exponential Functions and Sequences Chapter Review &#8211; Page(348-350)<\/a><\/li>\n<li><a href=\"#Exponential_Functions_and_Sequences_Chapter_Test\">Exponential Functions and Sequences Chapter Test &#8211; Page 351<\/a><\/li>\n<li><a href=\"#Exponential_Functions_and_Sequences_Cumulative_Assessment\">Exponential Functions and Sequences Cumulative Assessment &#8211; Page(352-353)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Exponential_Functions_and_Sequences_Maintaining_Mathematical_Proficiency\"><\/a>Exponential Functions and Sequences Maintaining Mathematical Proficiency<\/h3>\n<p><b>Evaluate the expression.<\/b><\/p>\n<p>Question 1.<br \/>\n12(\\(\\frac{14}{2}\\)) &#8211; 3<sup>3<\/sup> + 15 &#8211; 9<sup>2<\/sup><\/p>\n<p>Question 2.<br \/>\n5<sup>3<\/sup> \u2022 8 \u00f7 2<sup>2<\/sup> + 20 \u2022 3 &#8211; 4<\/p>\n<p>Question 3.<br \/>\n-7 + 16 \u00f7 2<sup>4<\/sup> + (10 &#8211; 4<sup>2<\/sup>)<\/p>\n<p><b>Find the square root(s).<\/b><\/p>\n<p>Question 4.<br \/>\n\\(\\sqrt{64}\\)<\/p>\n<p>Question 5.<br \/>\n&#8211;\\(\\sqrt{4}\\)<\/p>\n<p>Question 6.<br \/>\n&#8211;\\(\\sqrt{25}\\)<\/p>\n<p>Question 7.<br \/>\n\u00b1\\(\\sqrt{21}\\)<\/p>\n<p>Question 8.<br \/>\n12, 14, 16, 18, . . .<\/p>\n<p>Question 9.<br \/>\n6, 3, 0, -3, . . .<\/p>\n<p>Question 10.<br \/>\n22, 15, 8, 1, . . .<\/p>\n<p>Question 11.<br \/>\n<b>ABSTRACT REASONING<\/b><br \/>\nRecall that a perfect square is a number with integers as its square roots. Is the product of two perfect squares always a perfect square? Is the quotient of two perfect squares always a perfect square? Explain your reasoning.<\/p>\n<h3><a id=\"Exponential_Functions_and_Sequences_Mathematical_Practices\"><\/a>Exponential Functions and Sequences Mathematical Practices<\/h3>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 1.<br \/>\nA rabbit population over 8 consecutive years is given by 50, 80, 128, 205, 328, 524, 839, 1342. Find the population in the tenth year.<\/p>\n<p>Question 2.<br \/>\nThe sums of the numbers in the first eight rows of Pascal\u2019s Triangle are 1, 2, 4, 8, 16, 32, 64, 128. Find the sum of the numbers in the tenth row.<\/p>\n<h3><a id=\"Lesson_6.1_Properties_of_Exponents\"><\/a>Lesson 6.1 Properties of Exponents<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow can you write general rules involving properties of exponents?<\/p>\n<p><b>EXPLORATION 1<br \/>\nWriting Rules for Properties of Exponents<br \/>\nWork with a partner.<\/b><br \/>\na. What happens when you multiply two powers with the same base? Write the product of the two powers as a single power. Then write a general rule for finding the product of two powers with the same base.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38215\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 1\" width=\"525\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-1.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-1-300x40.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38214\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-1.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 1.1\" width=\"250\" height=\"225\" \/><br \/>\nb. What happens when you divide two powers with the same base? Write the quotient of the two powers as a single power. Then write a general rule for finding the quotient of two powers with the same base.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38216\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 2\" width=\"487\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-2.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-2-300x66.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><br \/>\nc. What happens when you find a power of a power? Write the expression as a single power. Then write a general rule for finding a power of a power.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38217\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 3\" width=\"512\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-3.png 512w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-3-300x41.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><br \/>\nd. What happens when you find a power of a product? Write the expression as the product of two powers. Then write a general rule for finding a power of a product.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38218\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-4.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 4\" width=\"527\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-4.png 527w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-4-300x40.png 300w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><br \/>\ne. What happens when you find a power of a quotient? Write the expression as the quotient of two powers. Then write a general rule for finding a power of a quotient.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38219\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 5\" width=\"504\" height=\"105\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-5.png 504w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-5-300x63.png 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 2.<br \/>\nHow can you write general rules involving properties of exponents?<\/p>\n<p>Question 3.<br \/>\nThere are 3<sup>3<\/sup> small cubes in the cube below. Write an expression for the number of small cubes in the large cube at the right.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38220\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6\" width=\"427\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.png 427w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6-300x137.png 300w\" sizes=\"(max-width: 427px) 100vw, 427px\" \/><\/p>\n<p><b>6.1 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Evaluate the expression.<\/b><\/p>\n<p>Question 1.<br \/>\n(-9)\u00b0<\/p>\n<p>Question 2.<br \/>\n3<sup>-3<\/sup><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38221\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 7\" width=\"47\" height=\"50\" \/><\/p>\n<p>Question 4.<br \/>\nSimplify the expression <img loading=\"lazy\" class=\"alignnone size-full wp-image-38224\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-8.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 8\" width=\"51\" height=\"45\" \/>. Write your answer using only positive exponents.<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Simplify the expression. Write your answer using only positive exponents.<\/b><\/p>\n<p>Question 5.<br \/>\n10<sup>4<\/sup> \u2022 10<sup>-6<\/sup><\/p>\n<p>Question 6.<br \/>\nx<sup>9<\/sup> \u2022 x<sup>-9<\/sup><\/p>\n<p>Question 7.<br \/>\n\\(\\frac{-5^{8}}{-5^{4}}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{y^{6}}{y^{7}}\\)<\/p>\n<p>Question 9.<br \/>\n(6<sup>-2<\/sup>)<sup>-1<\/sup><\/p>\n<p>Question 10.<br \/>\n(w<sup>12<\/sup>)<sup>5<\/sup><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Simplify the expression. Write your answer using only positive exponents.<\/b><\/p>\n<p>Question 11.<br \/>\n(10y)<sup>-3<\/sup><\/p>\n<p>Question 12.<br \/>\n(\\(-\\frac{4}{n}\\))<sup>5<\/sup><\/p>\n<p>Question 13.<br \/>\n(\\(\\frac{1}{2 k^{2}}\\))<sup>5<\/sup><\/p>\n<p>Question 14.<br \/>\n(\\(\\frac{6 c}{7}\\))<sup>-2<\/sup><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 15.<br \/>\nWrite two expressions that represent the area of a base of the cylinder in Example 5.<\/p>\n<p>Question 16.<br \/>\nIt takes the Sun about 2.3 \u00d7 10<sup>8<\/sup> years to orbit the center of the Milky Way. It takes Pluto about 2.5 \u00d7 10<sup>2<\/sup> years to orbit the Sun. How many times does Pluto orbit the Sun while the Sun completes one orbit around the center of the Milky Way? Write your answer in scientific notation.<\/p>\n<h3><a id=\"Properties_of_Exponents_6.1_Exercises\"><\/a>Properties of Exponents 6.1 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>VOCABULARY<\/b><br \/>\nWhich definitions or properties would you use to simplify the expression (4<sup>8<\/sup> \u2022 4<sup>-4<\/sup>)<sup>-2<\/sup>? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 1\" width=\"557\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-1.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-1-300x87.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>WRITING<\/b><br \/>\nExplain when and how to use the Power of a Product Property.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<b>WRITING<\/b><br \/>\nExplain when and how to use the Quotient of Powers Property.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43015\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 3\" width=\"562\" height=\"137\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-3.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-3-300x73.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 4.<br \/>\n<b>DIFFERENT WORDS, SAME QUESTION<\/b><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38222\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-8.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 8.1\" width=\"647\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-8.1.png 647w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-8.1-300x25.png 300w\" sizes=\"(max-width: 647px) 100vw, 647px\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 5\u201312, evaluate the expression. <\/b>(See Example 1.)<\/p>\n<p>Question 5.<br \/>\n(-7)\u00b0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 5\" width=\"109\" height=\"35\" \/><\/p>\n<p>Question 6.<br \/>\n4\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n5<sup>-4<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43013\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 7\" width=\"159\" height=\"61\" \/><\/p>\n<p>Question 8.<br \/>\n(-2)<sup>-5<\/sup><\/p>\n<p>Question 9.<br \/>\n\\(\\frac{2^{-4}}{4^{0}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 9\" width=\"188\" height=\"59\" \/><\/p>\n<p>Question 10.<br \/>\n\\(\\frac{5^{-1}}{-9^{0}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{-3^{-3}}{6^{-2}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 11\" width=\"266\" height=\"62\" \/><\/p>\n<p>Question 12.<br \/>\n\\(\\frac{(-8)^{-2}}{3^{-4}}\\)<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 13\u201322, simplify the expression. Write your answer using only positive exponents.<\/b><\/p>\n<p>Question 13.<br \/>\nx<sup>-7<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43010\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 13\" width=\"95\" height=\"52\" \/><\/p>\n<p>Question 14.<br \/>\ny\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n9x\u00b0y<sup>-3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 15\" width=\"200\" height=\"60\" \/><\/p>\n<p>Question 16.<br \/>\n15c<sup>-8<\/sup>d\u00b0<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{2^{-2} m^{-3}}{n^{0}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43008\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 17\" width=\"255\" height=\"60\" \/><\/p>\n<p>Question 18.<br \/>\n\\(\\frac{10^{0} r^{-11} s}{3^{2}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n\\(\\frac{4^{-3} a^{0}}{b^{-7}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43007\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 19\" width=\"197\" height=\"56\" \/><\/p>\n<p>Question 20.<br \/>\n\\(\\frac{p^{-8}}{7^{-2} q^{-9}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n\\(\\frac{2^{2} y^{-6}}{8^{-1} z^{0} x^{-7}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43006\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 21\" width=\"414\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-21.png 414w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-21-300x39.png 300w\" sizes=\"(max-width: 414px) 100vw, 414px\" \/><\/p>\n<p>Question 22.<br \/>\n\\(\\frac{13 x^{-5} y^{0}}{5^{-3} z^{-10}}\\)<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 23\u201332, simplify the expression. Write your answer using only positive exponents.<\/b><\/p>\n<p>Question 23.<br \/>\n\\(\\frac{5^{6}}{5^{2}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43005\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 23\" width=\"121\" height=\"108\" \/><\/p>\n<p>Question 24.<br \/>\n\\(\\frac{(-6)^{8}}{(-6)^{5}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n(-9)<sup>2<\/sup> \u2022 (-9)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 25\" width=\"245\" height=\"99\" \/><\/p>\n<p>Question 26.<br \/>\n4<sup>-5<\/sup> \u2022 4<sup>5<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n(p<sup>6<\/sup>)<sup>4<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43003\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 27\" width=\"122\" height=\"63\" \/><\/p>\n<p>Question 28.<br \/>\n(s<sup>-5<\/sup>)<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n6<sup>-8<\/sup> \u2022 6<sup>5<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43002\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 29\" width=\"174\" height=\"188\" \/><\/p>\n<p>Question 30.<br \/>\n-7 \u2022 (-7)<sup>-4<\/sup><\/p>\n<p>Question 31.<br \/>\n\\(\\frac{x^{5}}{x^{4}}\\) \u2022 x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43001\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 31\" width=\"174\" height=\"144\" \/><\/p>\n<p>Question 32.<br \/>\n\\(\\frac{z^{8} \\cdot z^{2}}{z^{5}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<b>USING PROPERTIES<\/b><br \/>\nA microscope magnifies an object 10<sup>5<\/sup> times. The length of an object is 10<sup>-7<\/sup> meter. What is its magnified length?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38223\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-8.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 8.2\" width=\"133\" height=\"206\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 33\" width=\"539\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-33.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-33-300x53.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 34.<br \/>\n<b>USING PROPERTIES<\/b><br \/>\nThe area of the rectangular computer chip is 112<sup>3<\/sup>b<sup>2<\/sup> square microns. What is the length?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38225\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 9\" width=\"170\" height=\"160\" \/><br \/>\nAnswer:<\/p>\n<p><b>ERROR ANALYSIS<br \/>\nIn Exercises 35 and 36, describe and correct the error in simplifying the expression.<\/b><\/p>\n<p>Question 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38226\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-10.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 10\" width=\"283\" height=\"97\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 35\" width=\"526\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-35.png 526w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-35-300x68.png 300w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><\/p>\n<p>Question 36.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38227\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 11\" width=\"286\" height=\"131\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 37\u201344, simplify the expression. Write your answer using only positive exponents.<\/b><\/p>\n<p>Question 37.<br \/>\n(-5z)<sup>3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 37\" width=\"173\" height=\"67\" \/><\/p>\n<p>Question 38.<br \/>\n(4x)<sup>-4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n(\\(\\frac{6}{n}\\))<sup>-2<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 39\" width=\"228\" height=\"61\" \/><br \/>\nAnswer:<\/p>\n<p>Question 40.<br \/>\n(\\(\\frac{-t}{3}\\))<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n(3s<sup>8<\/sup>)<sup>-5<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42996\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 41\" width=\"429\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-41.png 429w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-41-300x41.png 300w\" sizes=\"(max-width: 429px) 100vw, 429px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 42.<br \/>\n(-5p<sup>3<\/sup>)<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n(\\(-\\frac{w^{3}}{6}\\))<sup>-2<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42995\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 43\" width=\"518\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-43.png 518w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-43-300x36.png 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 44.<br \/>\n(\\(\\frac{1}{2 r^{6}}\\))<sup>-6<\/sup><\/p>\n<p>Question 45.<br \/>\n<b>USING PROPERTIES<\/b><br \/>\nWhich of the expressions represent the volume of the sphere? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38228\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-12.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 12\" width=\"153\" height=\"144\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38231\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 13\" width=\"327\" height=\"153\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-13.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-13-300x140.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 45\" width=\"556\" height=\"586\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-45.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-45-285x300.png 285w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 46.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nDiffusion is the movement of molecules from one location to another. The time t (in seconds) it takes molecules to diffuse a distance of x centimeters is given by t = \\(\\frac{x^{2}}{2 D}\\), where D is the diffusion coefficient. The diffusion coefficient for a drop of ink in water is about 10<sup>-5<\/sup> square centimeters per second. How long will it take the ink to diffuse 1 micrometer (10<sup>-4<\/sup> centimeter)?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38230\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-13.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 13.1\" width=\"110\" height=\"210\" \/><\/p>\n<p><b>In Exercises 47\u201350, simplify the expression. Write your answer using only positive exponents.<\/b><\/p>\n<p>Question 47.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38232\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-14.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 14\" width=\"83\" height=\"58\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42993\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 47\" width=\"459\" height=\"131\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-47.png 459w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-47-300x86.png 300w\" sizes=\"(max-width: 459px) 100vw, 459px\" \/><\/p>\n<p>Question 48.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38233\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 15\" width=\"97\" height=\"59\" \/><br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38234\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-16.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 16\" width=\"144\" height=\"57\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42992\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 49\" width=\"433\" height=\"549\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-49.png 433w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-49-237x300.png 237w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><\/p>\n<p>Question 50.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38235\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 17\" width=\"149\" height=\"64\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 51\u201354, evaluate the expression. Write your answer in scientific notation and standard form.<\/b><\/p>\n<p>Question 51.<br \/>\n(3 \u00d7 10<sup>2<\/sup>)(1.5 \u00d7 10<sup>-5<\/sup>)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 51\" width=\"434\" height=\"138\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-51.png 434w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-51-300x95.png 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><\/p>\n<p>Question 52.<br \/>\n(6.1 \u00d7 10<sup>-3<\/sup>)(8 \u00d7 10<sup>9<\/sup>)<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38236\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-18.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 18\" width=\"96\" height=\"52\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 53\" width=\"304\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-53.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-53-300x164.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><\/p>\n<p>Question 54.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38237\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 19\" width=\"101\" height=\"51\" \/><br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nIn 2012, on average, about 9.46 \u00d7 10<sup>-1<\/sup> pound of potatoes was produced for every 2.3 \u00d7 10<sup>-5<\/sup> acre harvested. How many pounds of potatoes on average were produced for each acre harvested? Write your answer in scientific notation and in standard form.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42989\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 55\" width=\"573\" height=\"222\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-55.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-55-300x116.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 56.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nThe speed of light is approximately 3 \u00d7 10<sup>5<\/sup> kilometers per second. How long does it take sunlight to reach Jupiter? Write your answer in scientific notation and in standard form.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38238\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-20.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 20\" width=\"408\" height=\"188\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-20.png 408w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-20-300x138.png 300w\" sizes=\"(max-width: 408px) 100vw, 408px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<b>MATHEMATICAL CONNECTIONS<\/b><br \/>\nConsider Cube A and Cube B.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38239\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 21\" width=\"222\" height=\"138\" \/><br \/>\na. Which property of exponents should you use to simplify an expression for the volume of each cube?<br \/>\nb. How can you use the Power of a Quotient Property to find how many times greater the volume of Cube B is than the volume of Cube A?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42988\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 57\" width=\"599\" height=\"208\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-57.png 599w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-57-300x104.png 300w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><\/p>\n<p>Question 58.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nA byte is a unit used to measure a computer\u2019s memory. The table shows the numbers of bytes in several units of measure.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38240\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-22.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 22\" width=\"408\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-22.png 408w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-22-300x73.png 300w\" sizes=\"(max-width: 408px) 100vw, 408px\" \/><br \/>\na. How many kilobytes are in 1 terabyte?<br \/>\nb. How many megabytes are in 16 gigabytes?<br \/>\nc. Another unit used to measure a computer\u2019s memory is a bit. There are 8 bits in a byte. How can you convert the number of bytes in each unit of measure given in the table to bits? Can you still use a base of 2? Explain.<br \/>\nAnswer:<\/p>\n<p><b>REWRITING EXPRESSIONS<br \/>\nIn Exercises 59\u201362, rewrite the expression as a power of a product.<\/b><\/p>\n<p>questions 59.<br \/>\n8a<sup>3<\/sup>b<sup>3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42987\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-59.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 59\" width=\"229\" height=\"33\" \/><\/p>\n<p>Question 60.<br \/>\n16r<sup>2<\/sup>s<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n64w<sup>18<\/sup>z<sup>12<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42986\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-61.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 61\" width=\"302\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-61.png 302w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-61-300x35.png 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><\/p>\n<p>Question 62.<br \/>\n81x<sup>4<\/sup>y<sup>8<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n<b>USING STRUCTURE<\/b><br \/>\nThe probability of rolling a 6 on a number cube is \\(\\frac{1}{6}\\). The probability of rolling a 6 twice in a row is (\\(\\frac{1}{6}\\))<sup>2<\/sup> = \\(\\frac{1}{36}\\).<br \/>\na. Write an expression that represents the probability of rolling a 6 n times in a row.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38241\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 23\" width=\"133\" height=\"131\" \/><br \/>\nb. What is the probability of rolling a 6 four times in a row?<br \/>\nc. What is the probability of flipping heads on a coin five times in a row? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42985\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-63.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 63\" width=\"537\" height=\"274\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-63.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-63-300x153.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Question 64.<br \/>\n<b>HOW DO YOU SEE IT?<\/b><br \/>\nThe shaded part of Figure n represents the portion of a piece of paper visible after folding the paper in half n times.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38242\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-24.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 24\" width=\"227\" height=\"228\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-24.png 227w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-24-150x150.png 150w\" sizes=\"(max-width: 227px) 100vw, 227px\" \/><br \/>\na. What fraction of the original piece of paper is each shaded part?<br \/>\nb. Rewrite each fraction from part (a) in the form 2x.<br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\n<b>REASONING<\/b><br \/>\nFind x and y when \\(\\frac{b^{x}}{b^{y}}\\) = b<sup>9<\/sup> and \\(\\frac{b^{x} \\cdot b^{2}}{b^{3 y}}\\) = b<sup>13<\/sup>. Explain how you found your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42984\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-65.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 65.1\" width=\"710\" height=\"335\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-65.1.png 710w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-65.1-300x142.png 300w\" sizes=\"(max-width: 710px) 100vw, 710px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42983\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-65.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 65.2\" width=\"298\" height=\"529\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-65.2.png 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-65.2-169x300.png 169w\" sizes=\"(max-width: 298px) 100vw, 298px\" \/><\/p>\n<p>Question 66.<br \/>\n<b>THOUGHT PROVOKING<\/b><br \/>\nWrite expressions for r and h so that the volume of the cone can be represented by the expression 27\u03c0x<sup>8<\/sup>. Find r and h.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38243\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 25\" width=\"154\" height=\"150\" \/><br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nOne of the smallest plant seeds comes from an orchid, and one of the largest plant seeds comes from a double coconut palm. A seed from an orchid has a mass of 10<sup>-6<\/sup> gram. The mass of a seed from a double coconut palm is 1010 times the mass of the seed from the orchid. Your friend says that the seed from the double coconut palm has a mass of about 1 kilogram. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42982\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-67.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 67\" width=\"530\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-67.png 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-67-300x113.png 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p>Question 68.<br \/>\n<b>CRITICAL THINKING<\/b><br \/>\nYour school is conducting a survey. Students can answer the questions in either part with \u201cagree\u201d or \u201cdisagree.\u201d<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-26.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 26\" width=\"342\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-26.png 342w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-26-300x146.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><br \/>\na. What power of 2 represents the number of different ways that a student can answer all the questions in Part 1?<br \/>\nb. What power of 2 represents the number of different ways that a student can answer all the questions on the entire survey?<br \/>\nc. The survey changes, and students can now answer \u201cagree,\u201d \u201cdisagree,\u201d or \u201cno opinion.\u201d How does this affect your answers in parts (a) and (b)?<br \/>\nAnswer:<\/p>\n<p>Question 69.<br \/>\n<b>ABSTRACT REASONING<\/b><br \/>\nCompare the values of a<sup>n<\/sup> and a<sup>-n<\/sup> when n &lt; 0, when n = 0, and when n &gt; 0 for<br \/>\n(a) a &gt; 1 and<br \/>\n(b) 0 &lt; a &lt; 1. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42981\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-69.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 69\" width=\"584\" height=\"286\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-69.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-69-300x147.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Find the square root(s).<\/b><\/p>\n<p>Question 70.<br \/>\n\\(\\sqrt{25}\\)<br \/>\nAnswer:<\/p>\n<p>Question 71.<br \/>\n&#8211;\\(\\sqrt{100}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42980\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-71.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 71\" width=\"438\" height=\"72\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-71.png 438w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-71-300x49.png 300w\" sizes=\"(max-width: 438px) 100vw, 438px\" \/><\/p>\n<p>Question 72.<br \/>\n\u00b1 \\(\\sqrt{\\frac{1}{64}}\\)<br \/>\nAnswer:<\/p>\n<p><b>Classify the real number in as many ways as possible.<\/b><\/p>\n<p>Question 73.<br \/>\n12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42979\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-73.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 73\" width=\"509\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-73.png 509w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-73-300x35.png 300w\" sizes=\"(max-width: 509px) 100vw, 509px\" \/><\/p>\n<p>Question 74.<br \/>\n\\(\\frac{65}{9}\\)<br \/>\nAnswer:<\/p>\n<p>Question 75.<br \/>\n\\(\\frac{\\pi}{4}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42978\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-75.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.1 Question 75\" width=\"413\" height=\"48\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-75.png 413w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.1-Question-75-300x35.png 300w\" sizes=\"(max-width: 413px) 100vw, 413px\" \/><\/p>\n<h3><a id=\"Lesson_6.2_Radicals_and_Rational_Exponents\"><\/a>Lesson 6.2 Radicals and Rational Exponents<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow can you write and evaluate an nth root of a number?<br \/>\nRecall that you cube a number as follows.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38245\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 27\" width=\"347\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-27.png 347w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-27-300x58.png 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><br \/>\nTo \u201cundo\u201d cubing a number, take the cube root of the number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38246\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-28.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 28\" width=\"442\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-28.png 442w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-28-300x52.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<p><b>EXPLORATION 1<br \/>\nFinding Cube Roots<br \/>\nWork with a partner.<\/b> Use a cube root symbol to write the side length of each cube. Then find the cube root. Check your answers by multiplying. Which cube is the largest? Which two cubes are the same size? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38247\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 29\" width=\"154\" height=\"135\" \/><br \/>\na. Volume = 27 ft<sup>3<\/sup><br \/>\nb. Volume = 125 cm<sup>3<\/sup><br \/>\nc. Volume = 3375 in.<sup>3<\/sup><br \/>\nd. Volume = 3.375 m<sup>3<\/sup><br \/>\ne. Volume = 1 yd<sup>3<\/sup><br \/>\nf. Volume = \\(\\frac{125}{8}\\) mm<sup>3<\/sup><\/p>\n<p><b>EXPLORATION 2<br \/>\nEstimating nth Roots<br \/>\nWork with a partner.<\/b> Estimate each positive nth root. Then match each nth root with the point on the number line. Justify your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38248\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-30.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 30.1\" width=\"256\" height=\"189\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38249\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-30.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 30\" width=\"583\" height=\"152\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-30.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-30-300x78.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you write and evaluate an nth root of a number?<\/p>\n<p>Question 4.<br \/>\nThe body mass m (in kilograms) of a dinosaur that walked on two feet can be modeled by<br \/>\nm = (0.00016)C<sup>2.73<\/sup><br \/>\nwhere C is the circumference (in millimeters) of the dinosaur\u2019s femur. The mass of a Tyrannosaurus rex was 4000 kilograms. Use a calculator to approximate the circumference of its femur.<\/p>\n<p><b>6.2 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Find the indicated real nth root(s) of a.<\/b><\/p>\n<p>Question 1.<br \/>\nn = 3, a = -125<\/p>\n<p>Question 2.<br \/>\nn = 6, a = 64<\/p>\n<p><b>Evaluate the expression.<\/b><\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt[3]{-125}\\)<\/p>\n<p>Question 4.<br \/>\n(-64)<sup>2 \/ 3<\/sup><\/p>\n<p>Question 5.<br \/>\n9<sup>5 \/ 2<\/sup><\/p>\n<p>Question 6.<br \/>\n256<sup>3 \/ 4<\/sup><\/p>\n<p>Question 7.<br \/>\n<b>WHAT IF?<\/b> In Example 4, the volume of the beach ball is 17,000 cubic inches. Find the radius to the nearest inch. Use 3.14 for \u03c0.<\/p>\n<p>Question 8.<br \/>\nThe average cost of college tuition increases from $8500 to $13,500 over a period of 8 years. Find the annual inflation rate to the nearest tenth of a percent.<\/p>\n<h3><a id=\"Radicals_and_Rational_Exponents_6.2_Exercises\"><\/a>Radicals and Rational Exponents 6.2 Exercises<\/h3>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p>Question 1.<br \/>\n<b>WRITING<\/b><br \/>\nExplain how to evaluate 81<sup>1 \/ 4<\/sup>.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42977\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 1\" width=\"564\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-1.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-1-300x30.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>WHICH ONE DOESN\u2019T BELONG?<\/b><br \/>\nWhich expression does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38250\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 31\" width=\"467\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-31.png 467w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-31-300x35.png 300w\" sizes=\"(max-width: 467px) 100vw, 467px\" \/><br \/>\nAnswer:<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3 and 4, rewrite the expression in rational exponent form.<\/b><\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt{10}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42976\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 3\" width=\"127\" height=\"35\" \/><\/p>\n<p>Question 4.<br \/>\n\\(\\sqrt[5]{34}\\)<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 5 and 6, rewrite the expression in radical form.<\/b><\/p>\n<p>Question 5.<br \/>\n15<sup>1 \/ 3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42975\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 5\" width=\"127\" height=\"33\" \/><\/p>\n<p>Question 6.<br \/>\n140<sup>1 \/ 8<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 7\u201310, find the indicated real nth root(s) of a.<\/b><\/p>\n<p>Question 7.<br \/>\nn = 2, a = 36<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42974\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 7\" width=\"577\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-7.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-7-300x43.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 8.<br \/>\nn = 4, a = 81<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nn = 3, a = 1000<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42973\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 9\" width=\"518\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-9.png 518w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-9-300x51.png 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><\/p>\n<p>Question 10.<br \/>\nn = 9, a = -512<br \/>\nAnswer:<\/p>\n<p><b>MATHEMATICAL CONNECTIONS<br \/>\nIn Exercises 11 and 12, find the dimensions of the cube. Check your answer.<\/b><\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38251\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-32.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 32\" width=\"146\" height=\"154\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42972\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 11\" width=\"432\" height=\"182\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-11.png 432w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-11-300x126.png 300w\" sizes=\"(max-width: 432px) 100vw, 432px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38252\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 33\" width=\"160\" height=\"158\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 13\u201318, evaluate the expression.<\/b><\/p>\n<p>Question 13.<br \/>\n\\(\\sqrt[4]{256}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42971\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 13\" width=\"234\" height=\"70\" \/><\/p>\n<p>Question 14.<br \/>\n\\(\\sqrt[3]{-216}\\)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n\\(\\sqrt[3]{-343}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42970\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 15\" width=\"319\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-15.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-15-300x67.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><\/p>\n<p>Question 16.<br \/>\n&#8211;\\(\\sqrt[5]{1024}\\)<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n128<sup>1 \/ 7<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42969\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 17\" width=\"338\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-17.png 338w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-17-300x95.png 300w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><\/p>\n<p>Question 18.<br \/>\n(-64)<sup>1 \/ 2<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 19 and 20, rewrite the expression in rational exponent form.<\/b><\/p>\n<p>Question 19.<br \/>\n(\\(\\sqrt[5]{8}\\))<sup>4<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42968\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 19\" width=\"158\" height=\"73\" \/><\/p>\n<p>Question 20.<br \/>\n(\\(\\sqrt[5]{-21}\\))<sup>6<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 21 and 22, rewrite the expression in radical form.<\/b><\/p>\n<p>Question 21.<br \/>\n(-4)<sup>2 \/ 7<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42967\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 21\" width=\"192\" height=\"67\" \/><\/p>\n<p>Question 22.<br \/>\n9<sup>5 \/ 2<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 23\u201328, evaluate the expression.<\/b><\/p>\n<p>Question 23.<br \/>\n32<sup>3 \/ 5<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42966\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 23\" width=\"152\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-23.png 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-23-150x100.png 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><\/p>\n<p>Question 24.<br \/>\n125<sup>2 \/ 3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n(-36)<sup>3 \/ 2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42965\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 25\" width=\"571\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-25.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-25-300x45.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 26.<br \/>\n(-243)<sup>2 \/ 5<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n(-128)<sup>5 \/ 7<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42964\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 27\" width=\"240\" height=\"100\" \/><\/p>\n<p>Question 28.<br \/>\n343<sup>4 \/ 3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<b>ERROR ANALYSIS<\/b><br \/>\nDescribe and correct the error in rewriting the expression in rational exponent form.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38253\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-34.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 34\" width=\"238\" height=\"89\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42963\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 29\" width=\"428\" height=\"96\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-29.png 428w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-29-300x67.png 300w\" sizes=\"(max-width: 428px) 100vw, 428px\" \/><\/p>\n<p>Question 30.<br \/>\n<b>ERROR ANALYSIS<\/b> Describe and correct the error in evaluating the expression.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38254\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 35\" width=\"289\" height=\"121\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 31\u201334, evaluate the expression.<\/b><\/p>\n<p>Question 31.<br \/>\n(\\(\\frac{1}{1000}\\))<sup>1 \/ 3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42961\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 31\" width=\"346\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-31.png 346w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-31-300x68.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><\/p>\n<p>Question 32.<br \/>\n(\\(\\frac{1}{64}\\))<sup>1 \/ 6<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n(27)-<sup>2 \/ 3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42960\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 33\" width=\"355\" height=\"74\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-33.png 355w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-33-300x63.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><\/p>\n<p>Question 34.<br \/>\n(9)-<sup>5 \/ 2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nA math club is having a bake sale. Find the area of the bake sale sign.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38255\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-36.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 36\" width=\"279\" height=\"183\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42959\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 35\" width=\"427\" height=\"246\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-35.png 427w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-35-300x173.png 300w\" sizes=\"(max-width: 427px) 100vw, 427px\" \/><\/p>\n<p>Question 36.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nThe volume of a cube-shaped box is 27<sup>5<\/sup> cubic millimeters. Find the length of one side of the box.<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> The radius r of the base of a cone is given by the equation r = (\\(\\frac{3 V}{\\pi h}\\))<sup>1 \/ 2<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38256\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 37\" width=\"208\" height=\"183\" \/><br \/>\nwhere V is the volume of the cone and h is the height of the cone. Find the radius of the paper cup to the nearest inch. Use 3.14 for \u03c0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42958\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 37\" width=\"551\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-37.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-37-300x54.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 38.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe volume of a sphere is given by the equation V = \\(\\frac{1}{6 \\sqrt{\\pi}}\\)S<sup>3 \/ 2<\/sup>, where S is the surface area of the sphere. Find the volume of a sphere, to the nearest cubic meter, that has a surface area of 60 square meters. Use 3.14 for \u03c0.<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<b>WRITING<\/b><br \/>\nExplain how to write (\\(\\sqrt[n]{a}\\))<sup>m<\/sup> in rational exponent form.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42957\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 39\" width=\"568\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-39.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-39-300x43.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 40.<br \/>\n<b>HOW DO YOU SEE IT?<\/b><br \/>\nWrite an expression in rational exponent form that represents the side length of the square.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38257\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-38.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 38\" width=\"140\" height=\"125\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 41 and 42, use the formula r = (\\(\\frac{F}{P}\\))<sup>1 \/ n<\/sup> &#8211; 1 to find the annual inflation rate to the nearest tenth of a percent.<\/b><\/p>\n<p>Question 41.<br \/>\nA farm increases in value from $800,000 to $1,100,000 over a period of 6 years.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42956\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 41\" width=\"376\" height=\"226\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-41.png 376w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-41-300x180.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/p>\n<p>Question 42.<br \/>\nThe cost of a gallon of gas increases from $1.46 to $3.53 over a period of 10 years.<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<b>REASONING<\/b><br \/>\nFor what values of x is x = x<sup>1 \/ 5<\/sup>?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42955\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 43\" width=\"540\" height=\"69\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-43.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-43-300x38.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 44.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nYour friend says that for a real number a and a positive integer n, the value of \\(\\sqrt[n]{a}\\) is always positive and the value of &#8211;\\(\\sqrt[n]{a}\\) is always negative. Is your friend correct? Explain.<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 45\u201348, simplify the expression.<\/b><\/p>\n<p>Question 45.<br \/>\n(y<sup>1 \/ 6<\/sup>)<sup>3<\/sup> \u2022 x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42954\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 45\" width=\"527\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-45.png 527w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-45-300x98.png 300w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><\/p>\n<p>Question 46.<br \/>\n(y \u2022 y<sup>1 \/ 3<\/sup>)<sup>3 \/ 2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\nx \u2022 \\(\\sqrt[3]{y^{6}}\\) + y<sup>2<\/sup> \u2022 \\(\\sqrt[3]{x^{3}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42953\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 47\" width=\"409\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-47.png 409w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-47-300x133.png 300w\" sizes=\"(max-width: 409px) 100vw, 409px\" \/><\/p>\n<p>Question 48.<br \/>\n(x<sup>1 \/ 3<\/sup> \u2022 y<sup>1 \/ 2<\/sup>)<sup>9<\/sup> \u2022 \\(\\sqrt{y}\\)<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nThe formula for the volume of a regular dodecahedron is V \u2248 7.66\u2113<sup>3<\/sup>, where \u2113 is the length of an edge. The volume of the dodecahedron is 20 cubic feet. Estimate the edge length.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38258\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 39\" width=\"165\" height=\"150\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42952\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 49\" width=\"499\" height=\"294\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-49.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-49-300x177.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p>Question 50.<br \/>\n<b>THOUGHT PROVOKING<\/b><br \/>\nFind a formula (for instance, from geometry or physics) that contains a radical. Rewrite the formula using rational exponents.<br \/>\nAnswer:<\/p>\n<p><b>ABSTRACT REASONING<br \/>\nIn Exercises 51\u201356, let x be a non negative real number. Determine whether the statement is always, sometimes, or never true. Justify your answer.<\/b><br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n(x<sup>1 \/ 3<\/sup>)<sup>3<\/sup> = x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42951\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 51\" width=\"514\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-51.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-51-300x50.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p>Question 52.<br \/>\nx<sup>1 \/ 3<\/sup> = x<sup>-3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\nx<sup>1 \/ 3<\/sup> = \\(\\sqrt[3]{x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42950\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 53\" width=\"502\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-53.png 502w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-53-300x39.png 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><\/p>\n<p>Question 54.<br \/>\nx = x<sup>1 \/ 3<\/sup> \u2022 x<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38259\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-40.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 40\" width=\"83\" height=\"51\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42949\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 55\" width=\"571\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-55.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-55-300x137.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Evaluate the function when x = \u22123, 0, and 8.<\/b>(Section 3.3)<\/p>\n<p>Question 57.<br \/>\nf(x) = 2x &#8211; 10<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42948\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 57\" width=\"439\" height=\"319\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-57.png 439w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-57-300x218.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><\/p>\n<p>Question 58.<br \/>\nw(x) = -5x &#8211; 1<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\nh(x) = 13 &#8211; x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42947\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-59.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.2 Question 59\" width=\"572\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-59.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.2-Question-59-300x89.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 60.<br \/>\ng(x) = 8x + 16<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_6.3_Exponential_Functions\"><\/a>Lesson 6.3 Exponential Functions<\/h3>\n<p><b>Essential Question<br \/>\nWhat are some of the characteristics of the graph of an exponential function?<br \/>\nEXPLORATION 1<br \/>\nExploring an Exponential Function<br \/>\nWork with a partner.<\/b> Copy and complete each table for the exponential function y = 16(2)<sup>x<\/sup>. In each table, what do you notice about the values of x? What do you notice about the values of y?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38260\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 41\" width=\"389\" height=\"435\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-41.png 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-41-268x300.png 268w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p><b>EXPLORATION 2<br \/>\nExploring an Exponential Function<br \/>\nWork with a partner. <\/b>Repeat Exploration 1 for the exponential function y = 16(\\(\\frac{1}{2}\\))<sup>x<\/sup>. Do you think the statement below is true for any exponential function? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38261\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-42.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 42\" width=\"258\" height=\"189\" \/><br \/>\n\u201cAs the independent variable x changes by a constant amount, the dependent variable y is multiplied by a constant factor.\u201d<\/p>\n<p><b>EXPLORATION 3<br \/>\nGraphing Exponential Functions<br \/>\nWork with a partner. <\/b>Sketch the graphs of the functions given in Explorations 1 and 2. How are the graphs similar? How are they different?<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 4.<br \/>\nWhat are some of the characteristics of the graph of an exponential function?<\/p>\n<p>Question 5.<br \/>\nSketch the graph of each exponential function. Does each graph have the characteristics you described in Question 4? Explain your reasoning.<br \/>\na. y = 2<sup>x<\/sup><br \/>\nb. y = 2(3)<sup>x<\/sup><br \/>\nc. y = 3(1.5)<sup>x<\/sup><br \/>\nd. y = (\\(\\frac{1}{2}\\))<sup>x<\/sup><br \/>\ne. y = 3(\\(\\frac{1}{2}\\))<sup>x<\/sup><br \/>\nf. y = 2(\\(\\frac{3}{4}\\))<sup>x<\/sup><\/p>\n<p><b>6.3 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Does the table represent a linear or an exponential function? Explain.<\/b><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38262\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 43\" width=\"238\" height=\"73\" \/><\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38263\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-44.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 44\" width=\"233\" height=\"76\" \/><\/p>\n<p><b>Evaluate the function when x = \u22122, 0, and \\(\\frac{1}{2}\\).<\/b><\/p>\n<p>Question 3.<br \/>\ny = 2(9)<sup>x<\/sup><\/p>\n<p>Question 4.<br \/>\ny = 1.5(2)<sup>x<\/sup><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Graph the function. Compare the graph to the graph of the parent function. Describe the domain and range of f.<\/b><\/p>\n<p>Question 5.<br \/>\nf(x) = -2(4)<sup>x<\/sup><\/p>\n<p>Question 6.<br \/>\nf(x) = 2(\\(\\frac{1}{4}\\))<sup>x<\/sup><\/p>\n<p><b>Graph the function. Describe the domain and range.<\/b><\/p>\n<p>Question 7.<br \/>\ny = -2(3)<sup>x + 2<\/sup> &#8211; 1<\/p>\n<p>Question 8.<br \/>\nf(x) = (0.25)<sup>x<\/sup> + 3<\/p>\n<p>Question 9.<br \/>\n<b>WHAT IF? <\/b>In Example 6, the dependent variable of g is multiplied by 3 for every 1 unit the independent variable x increases. Graph g when g(0) = 4. Compare g and the function f from Example 3 over the interval x = 0 to x = 2.<\/p>\n<p>Question 10.<br \/>\nA bacterial population y after x days can be represented by an exponential function whose graph passes through (0, 100) and (1, 200).<br \/>\n(a) Write a function that represents the population.<br \/>\n(b) Find the population after 6 days.<br \/>\n(c) Does this bacterial population grow faster than the bacterial population in Example 7? Explain.<\/p>\n<h3><a id=\"Exponential_Functions_6.3_Exercises\"><\/a>Exponential Functions 6.3 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>OPEN-ENDED<\/b><br \/>\nSketch an increasing exponential function whose graph has a y-intercept of 2.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42946\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 1\" width=\"261\" height=\"294\" \/><\/p>\n<p>Question 2.<br \/>\n<b>REASONING<\/b><br \/>\nWhy is a the y-intercept of the graph of the function y = ab<sup>x<\/sup>?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<b>WRITING<\/b><br \/>\nCompare the graph of y = 2(5)<sup>x<\/sup> with the graph of y = 5<sup>x<\/sup>.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42945\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 3\" width=\"554\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-3.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-3-300x78.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 4.<br \/>\n<b>WHICH ONE DOESN\u2019T BELONG?<\/b><br \/>\nWhich equation does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38264\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 45\" width=\"446\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-45.png 446w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-45-300x38.png 300w\" sizes=\"(max-width: 446px) 100vw, 446px\" \/><br \/>\nAnswer:<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 5\u201310, determine whether the equation represents an exponential function. Explain.<\/b><\/p>\n<p>Question 5.<br \/>\ny = 4(7)<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42944\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 5\" width=\"543\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-5.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-5-300x34.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 6.<br \/>\ny = -6x<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\ny = 2x<sup>3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42943\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 7\" width=\"508\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-7.png 508w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-7-300x35.png 300w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><\/p>\n<p>Question 8.<br \/>\ny = -3x<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ny = 9(-5)<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42942\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 9\" width=\"572\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-9.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-9-300x46.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 10.<br \/>\ny = \\(\\frac{1}{2}\\)(1)<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 11\u201314, determine whether the table represents a linear or an exponential function. Explain.\u00a0<\/b><\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38265\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-46.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 46\" width=\"125\" height=\"163\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42941\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 11\" width=\"542\" height=\"235\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-11.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-11-300x130.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38266\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 47\" width=\"121\" height=\"164\" \/><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38267\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-48.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 48\" width=\"279\" height=\"74\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42940\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 13\" width=\"548\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-13.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-13-300x112.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38268\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 49\" width=\"275\" height=\"75\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 15\u201320, evaluate the function for the given value of x.<\/b><\/p>\n<p>Question 15.<br \/>\ny = 3<sup>x<\/sup>; x = 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42939\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 15\" width=\"119\" height=\"62\" \/><\/p>\n<p>Question 16.<br \/>\nf(x) = 3(2)<sup>x<\/sup>; x = -1<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\ny = -4(5)<sup>x<\/sup>; x = 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42938\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 17\" width=\"138\" height=\"132\" \/><\/p>\n<p>Question 18.<br \/>\nf(x) = 0.5<sup>x<\/sup>; x = -3<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nf(x) = \\(\\frac{1}{3}\\)(6)<sup>x<\/sup>; x = 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42937\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 19\" width=\"268\" height=\"103\" \/><\/p>\n<p>Question 20.<br \/>\ny = \\(\\frac{1}{4}\\)(4)<sup>x<\/sup>; x = \\(\\frac{3}{2}\\)<br \/>\nAnswer:<\/p>\n<p><b>USING STRUCTURE<br \/>\nIn Exercises 21\u201324, match the function with its graph.<\/b><\/p>\n<p>Question 21.<br \/>\nf(x) = 2(0.5)<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42936\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 21\" width=\"579\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-21.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-21-300x74.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 22.<br \/>\ny = -2(0.5)<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\ny = 2(2)<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42935\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 23\" width=\"541\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-23.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-23-300x80.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 24.<br \/>\nf(x) = -2(2)<sup>x<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38269\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-50.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 50\" width=\"383\" height=\"318\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-50.png 383w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-50-300x249.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 25\u201330, graph the function. Compare the graph to the graph of the parent function. Describe the domain and range of f.<\/b><\/p>\n<p>Question 25.<br \/>\nf (x) = 3(0.5)<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42934\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 25\" width=\"599\" height=\"565\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-25.png 599w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-25-300x283.png 300w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><\/p>\n<p>Question 26.<br \/>\nf(x) = -4x<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nf(x) = -2(7)<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42933\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 27\" width=\"588\" height=\"572\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-27.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-27-300x292.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 28.<br \/>\nf(x) = 6 (\\(\\frac{1}{3}\\))<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nf(x) = \\(\\frac{1}{2}\\)(8)<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42932\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 29\" width=\"581\" height=\"614\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-29.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-29-284x300.png 284w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 30.<br \/>\nf (x) = \\(\\frac{3}{2}\\)(0.25)<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 31\u201336, graph the function. Describe the domain and range.<\/b><\/p>\n<p>Question 31.<br \/>\nf(x) = 3<sup>x<\/sup> &#8211; 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42931\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 31\" width=\"562\" height=\"469\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-31.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-31-300x250.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 32.<br \/>\nf(x) = 4<sup>x + 3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\ny = 5<sup>x &#8211; 2<\/sup> + 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42930\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 33\" width=\"536\" height=\"471\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-33.png 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-33-300x264.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Question 34.<br \/>\ny = &#8211; (\\(\\frac{1}{2}\\))<sup>x + 1<\/sup> &#8211; 3<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\ny = -8(0.75)<sup>x + 2<\/sup> &#8211; 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42929\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 35\" width=\"668\" height=\"642\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-35.png 668w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-35-300x288.png 300w\" sizes=\"(max-width: 668px) 100vw, 668px\" \/><\/p>\n<p>Question 36.<br \/>\nf(x) = 3(6)<sup>x &#8211; 1<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 37\u201340, compare the graphs. Find the value of h, k, or a.<\/b><\/p>\n<p>Question 37.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38271\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 51\" width=\"149\" height=\"171\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 37\" width=\"584\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-37.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-37-300x47.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38270\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-51.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 51.1\" width=\"167\" height=\"180\" \/><br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-52.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 52\" width=\"167\" height=\"172\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42927\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 39\" width=\"549\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-39.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-39-300x34.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 40.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38273\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 53\" width=\"167\" height=\"215\" \/><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<b>ERROR ANALYSIS<\/b><br \/>\nDescribe and correct the error in evaluating the function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38274\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-54.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 54\" width=\"327\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-54.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-54-300x128.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42926\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 41\" width=\"534\" height=\"209\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-41.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-41-300x117.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Question 42.<br \/>\n<b>ERROR ANALYSIS<\/b><br \/>\nDescribe and correct the error in finding the domain and range of the function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38275\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 55\" width=\"362\" height=\"188\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-55.png 362w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-55-300x156.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 43 and 44, graph the function with the given description. Compare the function to f (x) = 0.5(4)<sup>x<\/sup> over the interval x = 0 to x = 2.<\/b><\/p>\n<p>Question 43.<br \/>\nAn exponential function g models a relationship in which the dependent variable is multiplied by 2.5 for every 1 unit the independent variable x increases. The value of the function at 0 is 8.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 43\" width=\"512\" height=\"469\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-43.png 512w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-43-300x275.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/p>\n<p>Question 44.<br \/>\nAn exponential function h models a relationship in which the dependent variable is multiplied by \\(\\frac{1}{2}\\) for every 1 unit the independent variable x increases. The value of the function at 0 is 32.<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nYou graph an exponential function on a calculator. You zoom in repeatedly to 25% of the screen size. The function y = 0.25<sup>x<\/sup> represents the percent (in decimal form) of the original screen display that you see, where x is the number of times you zoom in.<br \/>\na. Graph the function. Describe the domain and range.<br \/>\nb. Find and interpret the y-intercept.<br \/>\nc. You zoom in twice. What percent of the original screen do you see?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42924\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-45.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 45.1\" width=\"577\" height=\"638\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-45.1.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-45.1-271x300.png 271w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42923\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-45.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 45.2\" width=\"555\" height=\"286\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-45.2.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-45.2-300x155.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 46.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nA population y of coyotes in a national park triples every 20 years. The function y = 15(3)<sup>x<\/sup> represents the population, where x is the number of 20-year periods.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38276\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-56.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 56\" width=\"201\" height=\"162\" \/><br \/>\na. Graph the function. Describe the domain and range.<br \/>\nb. Find and interpret the y-intercept.<br \/>\nc. How many coyotes are in the national park in 40 years?<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 47\u201350, write an exponential function represented by the table or graph.<\/b><\/p>\n<p>Question 47.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38277\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 57\" width=\"229\" height=\"79\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42922\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 47\" width=\"563\" height=\"298\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-47.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-47-300x159.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 48.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38278\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-58.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 58\" width=\"254\" height=\"81\" \/><br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38279\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-59.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 59\" width=\"172\" height=\"175\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42921\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 49\" width=\"573\" height=\"323\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-49.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-49-300x169.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 50.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38280\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-60.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 60\" width=\"182\" height=\"178\" \/><br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe graph represents the number y of visitors to a new art gallery after x months.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38294\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-61.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 61\" width=\"224\" height=\"261\" \/><br \/>\na. Write an exponential function that represents this situation.<br \/>\nb. Approximate the number of visitors after 5 months.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42920\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 51\" width=\"580\" height=\"592\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-51.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-51-294x300.png 294w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 52.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nA sales report shows that 3300 gas grills were purchased from a chain of hardware stores last year. The store expects grill sales to increase 6% each year. About how many grills does the store expect to sell in Year 6? Use an equation to justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<b>WRITING<\/b><br \/>\nGraph the function f(x) = -2<sup>x<\/sup>. Then graph g(x) = -2<sup>x<\/sup> &#8211; 3. How are the y-intercept, domain, and range affected by the translation?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42919\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 53\" width=\"586\" height=\"554\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-53.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-53-300x284.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 54.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nYour friend says that the table represents an exponential function because y is multiplied by a constant factor. Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38295\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-62.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 62\" width=\"239\" height=\"70\" \/><br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<b>WRITING<\/b><br \/>\nDescribe the effect of a on the graph of y = a \u2022 2<sup>x<\/sup> when a is positive and when a is negative.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42918\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 55\" width=\"564\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-55.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-55-300x77.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 56.<br \/>\n<b>OPEN-ENDED<\/b><br \/>\nWrite a function whose graph is a horizontal translation of the graph of h(x) = 4<sup>x<\/sup>.<br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<b>USING STRUCTURE<\/b><br \/>\nThe graph of g is a translation 4 units up and 3 units right of the graph of f(x) = 5<sup>x<\/sup>. Write an equation for g.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42917\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 57\" width=\"535\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-57.png 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-57-300x33.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p>Question 58.<br \/>\n<b>HOW DO YOU SEE IT?<\/b> The exponential function y = V(x) represents the projected value of a stock x weeks after a corporation loses an important legal battle. The graph of the function is shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38296\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-63.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 63\" width=\"244\" height=\"237\" \/><br \/>\na. After how many weeks will the stock be worth $20?<br \/>\nb. Describe the change in the stock price from Week 1 to Week 3.<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n<b>USING GRAPHS<\/b><br \/>\nThe graph represents the exponential function f. Find f(7).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38297\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-64.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 64\" width=\"180\" height=\"177\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-59.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 59\" width=\"581\" height=\"362\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-59.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-59-300x187.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 60.<br \/>\n<b>THOUGHT PROVOKING<\/b><br \/>\nWrite a function of the form y = ab<sup>x<\/sup> that represents a real-life population. Explain the meaning of each of the constants a and b in the real-life context.<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n<b>REASONING<\/b><br \/>\nLet f(x) = ab<sup>x<\/sup>. Show that when x is increased by a constant k, the quotient \\(\\frac{f(x+k)}{f(x)}\\) is always the same regardless of the value of x.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-61.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 61\" width=\"405\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-61.png 405w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-61-300x52.png 300w\" sizes=\"(max-width: 405px) 100vw, 405px\" \/><\/p>\n<p>Question 62.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nA function g models a relationship in which the dependent variable is multiplied by 4 for every 2 units the independent variable increases. The value of the function at 0 is 5. Write an equation that represents the function.<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nWrite an exponential function f so that the slope from the point (0, f(0)) to the point (2, f(2)) is equal to 12.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42914\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-63.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 63.1\" width=\"489\" height=\"424\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-63.1.png 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-63.1-300x260.png 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-63.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 63.2\" width=\"526\" height=\"304\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-63.2.png 526w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-63.2-300x173.png 300w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Write the percent as a decimal.<\/b><\/p>\n<p>Question 64.<br \/>\n4%<br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\n35%<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-65.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 65\" width=\"189\" height=\"59\" \/><\/p>\n<p>Question 66.<br \/>\n128%<br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\n250%<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.3-Question-67.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.3 Question 67\" width=\"197\" height=\"55\" \/><\/p>\n<h3><a id=\"Lesson_6.4_Exponential_Growth_and_Decay\"><\/a>Lesson 6.4 Exponential Growth and Decay<\/h3>\n<p><b>Essential Question<\/b><br \/>\nWhat are some of the characteristics of exponential growth and exponential decay functions?<\/p>\n<p><b>EXPLORATION 1<br \/>\nPredicting a Future Event<br \/>\nWork with a partner.<\/b> It is estimated, that in 1782, there were about 100,000 nesting pairs of bald eagles in the United States. By the 1960s, this number had dropped to about 500 nesting pairs. In 1967, the bald eagle was declared an endangered species in the United States. With protection, the nesting pair population began to increase. Finally, in 2007, the bald eagle was removed from the list of endangered and threatened species.<br \/>\nDescribe the pattern shown in the graph. Is it exponential growth? Assume the pattern continues. When will the population return to that of the late 1700s? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38298\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-65.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 65\" width=\"375\" height=\"292\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-65.png 375w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-65-300x234.png 300w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38299\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-66.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 66\" width=\"248\" height=\"191\" \/><\/p>\n<p><b>EXPLORATION 2<br \/>\nDescribing a Decay Pattern<br \/>\nWork with a partner. <\/b>A forensic pathologist was called to estimate the time of death of a person. At midnight, the body temperature was 80.5\u00b0F and the room temperature was a constant 60\u00b0F. One hour later, the body temperature was 78.5\u00b0F.<br \/>\na. By what percent did the difference between the body temperature and the room temperature drop during the hour?<br \/>\nb. Assume that the original body temperature was 98.6\u00b0F. Use the percent decrease found in part (a) to make a table showing the decreases in body temperature. Use the table to estimate the time of death.<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nWhat are some of the characteristics of exponential growth and exponential decay functions?<\/p>\n<p>Question 4.<br \/>\nUse the Internet or some other reference to find an example of each type of function. Your examples should be different than those given in Explorations 1 and 2.<br \/>\na. exponential growth<br \/>\nb. exponential decay<\/p>\n<p><b>6.4 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 1.<br \/>\nA website has 500,000 members in 2010. The number y of members increases by 15% each year.<br \/>\n(a) Write an exponential growth function that represents the website membership t years after 2010.<br \/>\n(b) How many members will there be in 2016? Round your answer to the nearest ten thousand.<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Determine whether the table represents an exponential growth function, an exponential decay function, or neither. Explain.<\/b><\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38300\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-67.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 67\" width=\"237\" height=\"77\" \/><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38301\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-68.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 68\" width=\"232\" height=\"72\" \/><\/p>\n<p><b>Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change.<\/b><\/p>\n<p>Question 4.<br \/>\ny = 2(0.92)<sup>t<\/sup><\/p>\n<p>Question 5.<br \/>\nf(t) = (1.2)<sup>t<\/sup><\/p>\n<p><b>Rewrite the function to determine whether it represents exponential growth or exponential decay.<\/b><\/p>\n<p>Question 6.<br \/>\nf(t) = 3(1.02)<sup>10t<\/sup><\/p>\n<p>Question 7.<br \/>\ny = (0.95)<sup>t + 2<\/sup><\/p>\n<p>Question 8.<br \/>\nYou deposit $500 in a savings account that earns 9% annual interest compounded monthly. Write and graph a function that represents the balance y (in dollars) after t years.<\/p>\n<p>Question 9.<br \/>\n<b>WHAT IF?<\/b> The car loses 9% of its value every year.<br \/>\n(a) Write a function that represents the value y (in dollars) of the car after t years.<br \/>\n(b) Find the approximate monthly percent decrease in value.<br \/>\n(c) Graph the function from part (a). Use the graph to estimate the value of the car after 12 years. Round your answer to the nearest thousand.<\/p>\n<h3><a id=\"Exponential_Growth_and_Decay_6.4_Exercises\"><\/a>Exponential Growth and Decay 6.4 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>COMPLETE THE SENTENCE<\/b><br \/>\nIn the exponential growth function y = a(1 + r)<sup>t<\/sup>, the quantity r is called the ________.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42910\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 1\" width=\"569\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-1.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-1-300x32.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>VOCABULARY<\/b><br \/>\nWhat is the decay factor in the exponential decay function y = a(1 &#8211; r)<sup>t<\/sup>?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<b>VOCABULARY<\/b><br \/>\nCompare exponential growth and exponential decay.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42909\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 3\" width=\"551\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-3.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-3-300x60.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 4.<br \/>\n<b>WRITING<\/b><br \/>\nWhen does the function y = ab<sup>x<\/sup> represent exponential growth? exponential decay?<br \/>\nAnswer:<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 5\u201312, identify the initial amount a and the rate of growth r (as a percent) of the exponential function. Evaluate the function when t = 5. Round your answer to the nearest tenth.<\/b><\/p>\n<p>Question 5.<br \/>\ny = 350(1 + 0.75)<sup>t<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42908\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 5\" width=\"513\" height=\"235\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-5.png 513w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-5-300x137.png 300w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><\/p>\n<p>Question 6.<br \/>\ny = 10(1 + 0.4)<sup>t<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\ny = 25(1.2)<sup>t<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 7\" width=\"576\" height=\"341\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-7.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-7-300x178.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 8.<br \/>\ny = 12(1.05)<sup>t<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nf(t) = 1500(1.074)<sup>t<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 9\" width=\"524\" height=\"342\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-9.png 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-9-300x196.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><\/p>\n<p>Question 10.<br \/>\nh(t) = 175(1.028)<sup>t<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\ng(t) = 6.72(2)<sup>t<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 11\" width=\"521\" height=\"338\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-11.png 521w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-11-300x195.png 300w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><\/p>\n<p>Question 12.<br \/>\np(t) = 1.8<sup>t<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 13\u201316, write a function that represents the situation.<\/b><\/p>\n<p>Question 13.<br \/>\nSales of $10,000 increase by 65% each year.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 13\" width=\"551\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-13.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-13-300x108.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 14.<br \/>\nYour starting annual salary of $35,000 increases by 4% each year.<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nA population of 210,000 increases by 12.5% each year.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 15\" width=\"579\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-15.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-15-300x103.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 16.<br \/>\nAn item costs $4.50, and its price increases by 3.5% each year.<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nThe population of a city has been increasing by 2% annually. The sign shown is from the year 2000.<br \/>\na. Write an exponential growth function that represents the population t years after 2000.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38302\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-69.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 69\" width=\"179\" height=\"155\" \/><br \/>\nb. What will the population be in 2020? Round your answer to the nearest thousand.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42901\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 17\" width=\"586\" height=\"462\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-17.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-17-300x237.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 18.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nA young channel catfish weighs about 0.1 pound. During the next 8 weeks, its weight increases by about 23% each week.<br \/>\na. Write an exponential growth function that represents the weight of the catfish after t weeks during the 8-week period.<br \/>\nb. About how much will the catfish weigh after 4 weeks? Round your answer to the nearest thousandth.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38303\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-70.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 70\" width=\"291\" height=\"114\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 19\u201326, identify the initial amount a and the rate of decay r (as a percent) of the exponential function. Evaluate the function when t = 3. Round your answer to the nearest tenth.<\/b><\/p>\n<p>Question 19.<br \/>\ny = 575(1 &#8211; 0.6)<sup>t<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 19\" width=\"514\" height=\"423\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-19.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-19-300x247.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p>Question 20.<br \/>\ny = 8(1 &#8211; 0.15)<sup>t<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\ng(t) = 240(0.75)<sup>t<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 21\" width=\"495\" height=\"423\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-21.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-21-300x256.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p>Question 22.<br \/>\nf(t) = 475(0.5)<sup>t<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nw(t) = 700(0.995)<sup>t<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42898\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 23\" width=\"515\" height=\"418\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-23.png 515w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-23-300x243.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><\/p>\n<p>Question 24.<br \/>\nh(t) = 1250(0.865)<sup>t<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\ny = (\\(\\frac{7}{8}\\))<sup>t<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 25\" width=\"488\" height=\"482\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-25.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-25-300x296.png 300w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><\/p>\n<p>Question 26.<br \/>\ny = 0.5 (\\(\\frac{3}{4}\\))<sup>t<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 27\u201330, write a function that represents the situation.<\/b><\/p>\n<p>Question 27.<br \/>\nA population of 100,000 decreases by 2% each year.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 27\" width=\"541\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-27.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-27-300x110.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 28.<br \/>\nA $900 sound system decreases in value by 9% each year.<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nA stock valued at $100 decreases in value by 9.5% each year.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 29\" width=\"564\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-29.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-29-300x106.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 30.<br \/>\nA company profit of $20,000 decreases by 13.4% each year.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<b>ERROR ANALYSIS<\/b> The growth rate of a bacterial culture is 150% each hour. Initially, there are 10 bacteria. Describe and correct the error in finding the number of bacteria in the culture after 8 hours.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38304\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-71.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 71\" width=\"369\" height=\"146\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-71.png 369w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-71-300x119.png 300w\" sizes=\"(max-width: 369px) 100vw, 369px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42894\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 31\" width=\"582\" height=\"267\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-31.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-31-300x138.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 32.<br \/>\n<b>ERROR ANALYSIS<\/b> You purchase a car in 2010 for $25,000. The value of the car decreases by 14% annually. Describe and correct the error in finding the value of the car in 2015.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38305\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-72.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 72\" width=\"362\" height=\"146\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-72.png 362w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-72-300x121.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 33\u201338, determine whether the table represents an exponential growth function, an exponential decay function, or neither. Explain.<\/b><\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38306\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-73.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 73\" width=\"125\" height=\"160\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42893\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 33\" width=\"496\" height=\"252\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-33.png 496w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-33-300x152.png 300w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><\/p>\n<p>Question 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38307\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-74.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 74\" width=\"125\" height=\"162\" \/><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38308\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-75.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 75\" width=\"129\" height=\"168\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42892\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 35\" width=\"575\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-35.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-35-300x136.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 36.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38309\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-76.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 76\" width=\"124\" height=\"164\" \/><br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38310\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-77.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 77\" width=\"120\" height=\"166\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42891\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 37\" width=\"495\" height=\"219\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-37.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-37-300x133.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p>Question 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38311\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-78.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 78\" width=\"126\" height=\"168\" \/><br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<b>ANALYZING RELATIONSHIPS<\/b><br \/>\nThe table shows the value of a camper t years after it is purchased.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38312\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-79.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 79\" width=\"169\" height=\"168\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-79.png 169w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-79-150x150.png 150w\" sizes=\"(max-width: 169px) 100vw, 169px\" \/><br \/>\na. Determine whether the table represents an exponential growth function, an exponential decay function, or neither.<br \/>\nb. What is the value of the camper after 5 years?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42890\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 39\" width=\"566\" height=\"332\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-39.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-39-300x176.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 40.<br \/>\n<b>ANALYZING RELATIONSHIPS<\/b><br \/>\nThe table shows the total numbers of visitors to a website t days after it is online.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38314\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-80.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 80\" width=\"376\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-80.png 376w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-80-300x69.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><br \/>\na. Determine whether the table represents an exponential growth function, an exponential decay function, or neither.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38313\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-80.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 80.1\" width=\"206\" height=\"182\" \/><br \/>\nb. How many people will have visited the website after it is online 47 days?<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 41\u201348, determine whether each function represents exponential growth or exponential decay. Identify the percent rate of change.<\/b><\/p>\n<p>Question 41.<br \/>\ny = 4(0.8)<sup>t<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42889\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 41\" width=\"554\" height=\"315\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-41.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-41-300x171.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 42.<br \/>\ny = 15(1.1)<sup>t<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\ny = 30(0.95)<sup>t<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42888\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 43\" width=\"561\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-43.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-43-300x167.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 44.<br \/>\ny = 5(1.08)<sup>t<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\nr(t) = 0.4(1.06)<sup>t<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42887\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 45\" width=\"555\" height=\"225\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-45.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-45-300x122.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 46.<br \/>\ns(t) = 0.65(0.48)<sup>t<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\ng(t) = 2 (\\(\\frac{5}{4}\\))<sup>t<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 47\" width=\"556\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-47.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-47-300x139.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 48.<br \/>\nm(t) = (\\(\\frac{4}{5}\\))<sup>t<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 49\u201356, rewrite the function to determine whether it represents exponential growth or exponential decay.<\/b><\/p>\n<p>Question 49.<br \/>\ny = (0.9)<sup>t &#8211; 4<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42885\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 49\" width=\"556\" height=\"286\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-49.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-49-300x154.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 50.<br \/>\ny = (1.4)<sup>t + 8<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\ny = 2(1.06)<sup>9t<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42884\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 51\" width=\"546\" height=\"165\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-51.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-51-300x91.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 52.<br \/>\ny = 5(0.82)<sup>t\/5<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\nx(t) = (1.45)<sup>t\/2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42883\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 53\" width=\"563\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-53.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-53-300x126.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 54.<br \/>\nf(t) = 0.4(1.16)<sup>t &#8211; 1<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\nb(t) = 4(0.55)<sup>t + 3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42882\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 55\" width=\"554\" height=\"233\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-55.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-55-300x126.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 56.<br \/>\nr(t) = (0.88)<sup>4r<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 57\u201360, write a function that represents the balance after t years.\u00a0<\/b><\/p>\n<p>Question 57.<br \/>\n$2000 deposit that earns 5% annual interest compounded quarterly<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 57\" width=\"239\" height=\"160\" \/><\/p>\n<p>Question 58.<br \/>\n$1400 deposit that earns 10% annual interest compounded semiannually<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n$6200 deposit that earns 8.4% annual interest compounded monthly<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42880\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-59.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 59\" width=\"238\" height=\"165\" \/><\/p>\n<p>Question 60.<br \/>\n$3500 deposit that earns 9.2% annual interest compounded quarterly<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nThe cross-sectional area of a tree 4.5 feet from the ground is called its basal area. The table shows the basal areas (in square inches) of Tree A over time.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38315\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-81.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 81\" width=\"409\" height=\"306\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-81.png 409w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-81-300x224.png 300w\" sizes=\"(max-width: 409px) 100vw, 409px\" \/><br \/>\na. Write functions that represent the basal areas of the trees after t years.<br \/>\nb. Graph the functions from part (a) in the same coordinate plane. Compare the basal areas.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42879\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-61.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 61.1\" width=\"598\" height=\"576\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-61.1.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-61.1-300x289.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-61.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 61.2\" width=\"604\" height=\"540\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-61.2.png 604w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-61.2-300x268.png 300w\" sizes=\"(max-width: 604px) 100vw, 604px\" \/><\/p>\n<p>Question 62.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nYou deposit $300 into an investment account that earns 12% annual interest compounded quarterly. The graph shows the balance of a savings account over time.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38316\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-82.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 82\" width=\"213\" height=\"224\" \/><br \/>\na. Write functions that represent the balances of the accounts after t years.<br \/>\nb. Graph the functions from part (a) in the same coordinate plane. Compare the account balances.<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n<b>PROBLEM SOLVING<\/b> A city has a population of 25,000. The population is expected to increase by 5.5% annually for the next decade.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38317\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-83.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 83\" width=\"339\" height=\"156\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-83.png 339w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-83-300x138.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><br \/>\na. Write a function that represents the population y after t years.<br \/>\nb. Find the approximate monthly percent increase in population.<br \/>\nc. Graph the function from part (a). Use the graph to estimate the population after 4 years.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-63.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 63.1\" width=\"666\" height=\"532\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-63.1.png 666w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-63.1-300x240.png 300w\" sizes=\"(max-width: 666px) 100vw, 666px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42876\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-63.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 63.2\" width=\"670\" height=\"483\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-63.2.png 670w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-63.2-300x216.png 300w\" sizes=\"(max-width: 670px) 100vw, 670px\" \/><\/p>\n<p>Question 64.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nPlutonium-238 is a material that generates steady heat due to decay and is used in power systems for some spacecraft. The function y = a(0.5)<sup>t\/x<\/sup> represents the amount y of a substance remaining after t years, where a is the initial amount and x is the length of the half-life (in years).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38318\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-84.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 84\" width=\"257\" height=\"194\" \/><br \/>\na. A scientist is studying a 3-gram sample. Write a function that represents the amount y of plutonium-238 after t years.<br \/>\nb. What is the yearly percent decrease of plutonium-238?<br \/>\nc. Graph the function from part (a). Use the graph to estimate the amount remaining after 12 years.<br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\n<b>COMPARING FUNCTIONS<\/b><br \/>\nThe three given functions describe the amount y of ibuprofen (in milligrams) in a person\u2019s bloodstream t hours after taking the dosage.<br \/>\ny \u2248 800(0.71)t<br \/>\ny \u2248 800(0.9943)<sup>60t<\/sup><br \/>\ny \u2248 800(0.843)<sup>2t<\/sup><br \/>\na. Show that these expressions are approximately equivalent.<br \/>\nb. Describe the information given by each of the functions.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-65.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 65.1\" width=\"534\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-65.1.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-65.1-300x171.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-65.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 65.2\" width=\"402\" height=\"482\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-65.2.png 402w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-65.2-250x300.png 250w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-65.3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 65.3\" width=\"567\" height=\"491\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-65.3.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-65.3-300x260.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 66.<br \/>\n<b>COMBINING FUNCTIONS<\/b> You deposit $9000 in a savings account that earns 3.6% annual interest compounded monthly. You also save $40 per month in a safe at home. Write a function C(t) = b(t) + h(t), where b(t) represents the balance of your savings account and h(t) represents the amount in your safe after t years. What does C(t) represent?<br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\n<b>NUMBER SENSE<\/b> During a flu epidemic, the number of sick people triples every week. What is the growth rate as a percent? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42871\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-67.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 67\" width=\"269\" height=\"174\" \/><\/p>\n<p>Question 68.<br \/>\n<b>HOW DO YOU SEE IT?<\/b> Match each situation with its graph. Explain your reasoning.<br \/>\na. A bacterial population doubles each hour.<br \/>\nb. The value of a computer decreases by 18% each year.<br \/>\nc. A deposit earns 11% annual interest compounded yearly.<br \/>\nd. A radioactive element decays 5.5% each year.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38319\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-85.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 85\" width=\"355\" height=\"274\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-85.png 355w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-85-300x232.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 69.<br \/>\n<b>WRITING<\/b> Give an example of an equation in the form y = ab<sup>x<\/sup> that does not represent an exponential growth function or an exponential decay function. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42870\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-69.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 69\" width=\"564\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-69.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-69-300x31.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 70.<br \/>\n<b>THOUGHT PROVOKING<\/b> Describe two account options into which you can deposit $1000 and earn compound interest. Write a function that represents the balance of each account after t years. Which account would you rather use? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 71.<br \/>\n<b>MAKING AN ARGUMENT<\/b> A store is having a sale on sweaters. On the first day, the prices of the sweaters are reduced by 20%. The prices will be reduced another 20% each day until the sweaters are sold. Your friend says the sweaters will be free on the fifth day. Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38320\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-86.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 86\" width=\"240\" height=\"219\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42869\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-71.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 71\" width=\"566\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-71.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-71-300x49.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 72.<br \/>\n<b>COMPARING FUNCTIONS<\/b> The graphs of f and g are shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38321\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-87.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 87\" width=\"217\" height=\"187\" \/><br \/>\na. Explain why f is an exponential growth function. Identify the rate of growth.<br \/>\nb. Describe the transformation from the graph of f to the graph of g. Determine the value of k.<br \/>\nc. The graph of g is the same as the graph of h(t) = f (t + r). Use properties of exponents to find the value of r.<br \/>\nAnswer:<\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Solve the equation. Check your solution.<\/b>(Section 1.3)<\/p>\n<p>Question 73.<br \/>\n8x + 12 = 4x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42868\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-73.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 73\" width=\"547\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-73.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-73-300x120.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Question 74.<br \/>\n5 &#8211; t = 7t + 21<br \/>\nAnswer:<\/p>\n<p>Question 75.<br \/>\n6(r &#8211; 2) = 2r + 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-75.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 75\" width=\"549\" height=\"379\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-75.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-75-300x207.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p><b>Find the slope and the y-intercept of the graph of the linear equation.<\/b>(Section 3.5)<\/p>\n<p>Question 76.<br \/>\ny = -6x + 7<br \/>\nAnswer:<\/p>\n<p>Question 77.<br \/>\ny = \\(\\frac{1}{4}\\)x + 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-77.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 77\" width=\"555\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-77.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-77-300x50.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 78.<br \/>\n3y = 6x &#8211; 12<br \/>\nAnswer:<\/p>\n<p>Question 79.<br \/>\n2y + x = 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42865\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-79.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.4 Question 79\" width=\"519\" height=\"299\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-79.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.4-Question-79-300x173.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<h3><a id=\"Exponential_Functions_and_Sequences_Study_Skills:_Analyzing_Your_Errors\"><\/a>Exponential Functions and Sequences Study Skills: Analyzing Your Errors<\/h3>\n<p><b>6.1\u20136.4 What Did You Learn?<\/b><\/p>\n<p><b>Core Vocabulary<\/b><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-38322\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-88.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 88\" width=\"633\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-88.png 633w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-88-300x54.png 300w\" sizes=\"(max-width: 633px) 100vw, 633px\" \/><\/p>\n<p><b>Core Concepts<\/b><br \/>\n<b>Section 6.1<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38323\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-89.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 89\" width=\"645\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-89.png 645w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-89-300x43.png 300w\" sizes=\"(max-width: 645px) 100vw, 645px\" \/><br \/>\n<b>Section 6.2<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-90.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 90\" width=\"574\" height=\"30\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-90.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-90-300x16.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><br \/>\n<b>Section 6.3<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38325\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-91.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 91\" width=\"673\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-91.png 673w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-91-300x16.png 300w\" sizes=\"(max-width: 673px) 100vw, 673px\" \/><br \/>\n<b>Section 6.4<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38326\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-92.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 92\" width=\"571\" height=\"48\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-92.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-92-300x25.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p><b>Mathematical Practices<\/b><\/p>\n<p>Question 1.<br \/>\nHow did you apply what you know to simplify the complicated situation in Exercise 56 on page 297?<\/p>\n<p>Question 2.<br \/>\nHow can you use previously established results to construct an argument in Exercise 44 on page 304?<\/p>\n<p>Question 3.<br \/>\nHow is the form of the function you wrote in Exercise 66 on page 322 related to the forms of other types of functions you have learned about in this course?<\/p>\n<p><b>Study Skills<\/b><\/p>\n<p><b>Analyzing Your Errors<\/b><\/p>\n<p><b>Misreading Directions<\/b><\/p>\n<ul>\n<li>What Happens: You incorrectly read or do not understand directions.<\/li>\n<li>How to Avoid This Error: Read the instructions for exercises at least twice and make sure you understand what they mean. Make this a habit and use it when taking tests.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-38327\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-93.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 93\" width=\"438\" height=\"323\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-93.png 438w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-93-300x221.png 300w\" sizes=\"(max-width: 438px) 100vw, 438px\" \/><\/p>\n<h3><a id=\"Exponential_Functions_6.1_-_6.4_Quiz\"><\/a>Exponential Functions 6.1 &#8211; 6.4 Quiz<\/h3>\n<p><b>Simplify the expression. Write your answer using only positive exponents.<\/b>(Section 6.1)<\/p>\n<p>Question 1.<br \/>\n3<sup>2<\/sup> \u2022 3<sup>4<\/sup><\/p>\n<p>Question 2.<br \/>\n(k<sup>4<\/sup>)<sup>-3<\/sup><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38328\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-94.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 94\" width=\"63\" height=\"59\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38329\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-95.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 95\" width=\"84\" height=\"58\" \/><\/p>\n<p><b>Evaluate the expression<\/b>.(Section 6.2)<\/p>\n<p>Question 5.<br \/>\n\\(\\sqrt[3]{27}\\)<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{1}{16}\\)<sup>1\/4<\/sup><\/p>\n<p>Question 7.<br \/>\n512<sup>2\/3<\/sup><\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt{4}\\)<sup>5<\/sup><\/p>\n<p><b>Graph the function. Describe the domain and range.<\/b>(Section 6.3)<\/p>\n<p>Question 9.<br \/>\ny = 5<sup>x<\/sup><\/p>\n<p>Question 10.<br \/>\ny = -2(\\(\\frac{1}{6}\\))<sup>x<\/sup><\/p>\n<p>Question 11.<br \/>\ny = 6(2)<sup>x &#8211; 4<\/sup> &#8211; 1<\/p>\n<p><b>Determine whether the table represents an exponential growth function, an exponential decay function, or neither. Explain.<\/b>(Section 6.4)<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38330\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-96.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 96\" width=\"235\" height=\"83\" \/><\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38331\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-97.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 97\" width=\"286\" height=\"85\" \/><\/p>\n<p><b>Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change.<\/b>(Section 6.4)<\/p>\n<p>Question 14.<br \/>\ny = 3(1.88)<sup>t<\/sup><\/p>\n<p>Question 15.<br \/>\nf(t) = \\(\\frac{1}{3}\\)(1.26)<sup>t<\/sup><\/p>\n<p>Question 16.<br \/>\nf(t) = 80(\\(\\frac{3}{5}\\))<sup>t<\/sup><\/p>\n<p>Question 17.<br \/>\nThe table shows several units of mass. (Section 6.1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38332\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-98.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 98\" width=\"787\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-98.png 787w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-98-300x38.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-98-768x98.png 768w\" sizes=\"(max-width: 787px) 100vw, 787px\" \/><br \/>\na. How many times larger is a kilogram than a nanogram? Write your answer using only positive exponents.<br \/>\nb. How many times smaller is a milligram than a hectogram? Write your answer using only positive exponents.<br \/>\nc. Which is greater, 10,000 milligrams or 1000 decigrams? Explain your reasoning.<\/p>\n<p>Question 18.<br \/>\nYou store blankets in a cedar chest. What is the volume of the cedar chest? (Section 6.2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38333\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-99.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 99\" width=\"284\" height=\"140\" \/><\/p>\n<p>Question 19.<br \/>\nThe function f(t) = 5(4)<sup>t<\/sup> represents the number of frogs in a pond after t years. (Section 6.3 and Section 6.4)<br \/>\na. Does the function represent exponential growth or exponential decay? Explain.<br \/>\nb. Graph the function. Describe the domain and range.<br \/>\nc. What is the yearly percent change? the approximate monthly percent change?<br \/>\nd. How many frogs are in the pond after 4 years?<\/p>\n<h3><a id=\"Lesson_6.5_Solving_Exponential_Functions\"><\/a>Lesson 6.5 Solving Exponential Functions<\/h3>\n<p><b>Essential Question<br \/>\nHow can you solve an exponential equation graphically?<br \/>\nEXPLORATION 1<br \/>\nSolving an Exponential Equation Graphically<br \/>\nWork with a partner.<\/b> Use a graphing calculator to solve the exponential equation 2.5<sup>x &#8211; 3<\/sup> = 6.25 graphically. Describe your process and explain how you determined the solution.<\/p>\n<p><b>EXPLORATION 2<br \/>\nThe Number of Solutions of an Exponential Equation<br \/>\nWork with a partner.<\/b><br \/>\na. Use a graphing calculator to graph the equation y = 2<sup>x<\/sup>.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38335\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-100.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 100\" width=\"252\" height=\"164\" \/><br \/>\nb. In the same viewing window, graph a linear equation (if possible) that does not intersect the graph of y = 2<sup>x<\/sup>.<br \/>\nc. In the same viewing window, graph a linear equation (if possible) that intersects the graph of y = 2<sup>x<\/sup> in more than one point.<br \/>\nd. Is it possible for an exponential equation to have no solution? more than one solution? Explain your reasoning.<\/p>\n<p><b>EXPLORATION 3<br \/>\nSolving Exponential Equations Graphically<br \/>\nWork with a partner. <\/b>Use a graphing calculator to solve each equation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38334\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-100.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 100.1\" width=\"253\" height=\"233\" \/><br \/>\na. 2<sup>x<\/sup> = \\(\\frac{1}{2}\\)<br \/>\nb. 2<sup>x + 1<\/sup> = 0<br \/>\nc. 2<sup>x<\/sup> = \\(\\sqrt{2}\\)<br \/>\nd. 3<sup>x<\/sup> = 9<br \/>\ne. 3<sup>x &#8211; 1<\/sup> = 0<br \/>\nf. 4<sup>2x<\/sup> = 2<br \/>\ng. 2<sup>x\/2<\/sup> = \\(\\frac{1}{4}\\)<br \/>\nh. 3<sup>x + 2<\/sup> = \\(\\frac{1}{9}\\)<br \/>\ni. 2<sup>x &#8211; 2<\/sup> = \\(\\frac{3}{2}\\)x &#8211; 2<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 4.<br \/>\nHow can you solve an exponential equation graphically?<\/p>\n<p>Question 5.<br \/>\nA population of 30 mice is expected to double each year. The number p of mice in the population each year is given by p = 30(2<sup>n<\/sup>). In how many years will there be 960 mice in the population?<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Solve the equation. Check your solution.<\/b><\/p>\n<p>Question 1.<br \/>\n2<sup>2x<\/sup> = 2<sup>6<\/sup><\/p>\n<p>Question 2.<br \/>\n5<sup>2x<\/sup> = 5<sup>x + 1<\/sup><\/p>\n<p>Question 3.<br \/>\n7<sup>3x + 5<\/sup> = 7<sup>x + 1<\/sup><\/p>\n<p><b>Solve the equation. Check your solution.<\/b><\/p>\n<p>Question 4.<br \/>\n4<sup>x<\/sup> = 256<\/p>\n<p>Question 5.<br \/>\n9<sup>2x<\/sup> = 3<sup>x &#8211; 6<\/sup><\/p>\n<p>Question 6.<br \/>\n4<sup>3x<\/sup> = 8<sup>x + 1<\/sup><\/p>\n<p>Question 7.<br \/>\n(\\(\\frac{1}{3}\\))<sup>x &#8211; 1<\/sup> = 27<\/p>\n<p><b>Use a graphing calculator to solve the equation.<\/b><\/p>\n<p>Question 8.<br \/>\n2<sup>x<\/sup> = 1.8<\/p>\n<p>Question 9.<br \/>\n4<sup>x &#8211; 3<\/sup> = x + 2<\/p>\n<p>Question 10.<br \/>\n(\\(\\frac{1}{4}\\))<sup>x<\/sup> = -2x &#8211; 3<\/p>\n<h3><a id=\"Solving_Exponential_Functions_6.5_Exercises\"><\/a>Solving Exponential Functions 6.5 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>WRITING<\/b><br \/>\nDescribe how to solve an exponential equation with unlike bases.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42864\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 1\" width=\"582\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-1.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-1-300x73.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>WHICH ONE DOESN\u2019T BELONG?<\/b> Which equation does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38336\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-101.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 101\" width=\"657\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-101.png 657w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-101-300x25.png 300w\" sizes=\"(max-width: 657px) 100vw, 657px\" \/><br \/>\nAnswer:<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3\u201312, solve the equation. Check your solution.<\/b><\/p>\n<p>Question 3.<br \/>\n4<sup>5x<\/sup> = 4<sup>10<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42863\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 3\" width=\"485\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-3.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-3-300x111.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/p>\n<p>Question 4.<br \/>\n7<sup>x &#8211; 4<\/sup> = 7<sup>8<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n3<sup>9x<\/sup> = 3<sup>7x + 8<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42862\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 5\" width=\"562\" height=\"255\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-5.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-5-300x136.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 6.<br \/>\n2<sup>4x<\/sup> = 2<sup>x + 9<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n2<sup>x<\/sup> = 64<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42861\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 7\" width=\"414\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-7.png 414w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-7-300x96.png 300w\" sizes=\"(max-width: 414px) 100vw, 414px\" \/><\/p>\n<p>Question 8.<br \/>\n3x = 243<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n7<sup>x &#8211; 5<\/sup> = 49<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42860\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 9\" width=\"486\" height=\"287\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-9.png 486w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-9-300x177.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p>Question 10.<br \/>\n216<sup>x<\/sup> = 6<sup>x + 10<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n64<sup>2x + 4<\/sup> = 16<sup>5x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42859\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 11\" width=\"568\" height=\"394\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-11.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-11-300x208.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 12.<br \/>\n27<sup>x<\/sup> = 9<sup>x &#8211; 2<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 13\u201318, solve the equation. Check your solution.<\/b><\/p>\n<p>Question 13.<br \/>\n(\\(\\frac{1}{5}\\))<sup>x<\/sup> = 125<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42858\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 13\" width=\"450\" height=\"323\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-13.png 450w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-13-300x215.png 300w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><\/p>\n<p>Question 14.<br \/>\n(\\(\\frac{1}{4}\\))<sup>x<\/sup> = 256<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n\\(\\frac{1}{128}\\) = 2<sup>5x + 3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 15\" width=\"493\" height=\"422\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-15.png 493w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-15-300x257.png 300w\" sizes=\"(max-width: 493px) 100vw, 493px\" \/><\/p>\n<p>Question 16.<br \/>\n3<sup>4x &#8211; 9<\/sup> = \\(\\frac{1}{243}\\)<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n36<sup>-3x + 3<\/sup> = (\\(\\frac{1}{216}\\))<sup>x + 1<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42856\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-17.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 17.1\" width=\"321\" height=\"510\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-17.1.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-17.1-189x300.png 189w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42855\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-17.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 17.2\" width=\"354\" height=\"441\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-17.2.png 354w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-17.2-241x300.png 241w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><\/p>\n<p>Question 18.<br \/>\n(\\(\\frac{1}{27}\\))<sup>4-x<\/sup> = 9<sup>2x-1<\/sup><br \/>\nAnswer:<\/p>\n<p><b>ERROR ANALYSIS<\/b> In Exercises 19 and 20, describe and correct the error in solving the exponential equation.<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38337\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-102.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 102\" width=\"275\" height=\"102\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42854\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 19\" width=\"572\" height=\"440\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-19.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-19-300x231.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38338\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-103.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 103\" width=\"272\" height=\"160\" \/><br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n2<sup>x<\/sup> = 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42853\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 21\" width=\"581\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-21.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-21-300x58.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 22.<br \/>\n4<sup>2x &#8211; 5<\/sup> = 6<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n5<sup>x + 2<\/sup> = 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42852\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 23\" width=\"579\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-23.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-23-300x58.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 24.<br \/>\n3<sup>-x &#8211; 1<\/sup> = 6<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38339\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-104.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 104\" width=\"411\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-104.png 411w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-104-300x207.png 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 25\u201336, use a graphing calculator to solve the equation.<\/b><\/p>\n<p>Question 25.<br \/>\n6<sup>x + 2<\/sup> = 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42851\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 25\" width=\"292\" height=\"240\" \/><\/p>\n<p>Question 26.<br \/>\n5<sup>x &#8211; 4<\/sup> = 8<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n(\\(\\frac{1}{2}\\))<sup>7x + 1<\/sup> = -9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42850\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 27\" width=\"563\" height=\"263\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-27.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-27-300x140.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 28.<br \/>\n(\\(\\frac{1}{3}\\))<sup>x + 3<\/sup> = 10<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n2<sup>x + 6<\/sup> = 2x + 15<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42849\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 29\" width=\"414\" height=\"244\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-29.png 414w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-29-300x177.png 300w\" sizes=\"(max-width: 414px) 100vw, 414px\" \/><\/p>\n<p>Question 30.<br \/>\n3x &#8211; 2 = 5<sup>x &#8211; 1<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n\\(\\frac{1}{2}\\)x &#8211; 1 = (\\(\\frac{1}{3}\\))<sup>2x &#8211; 1<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42848\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 31\" width=\"336\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-31.png 336w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-31-300x232.png 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><\/p>\n<p>Question 32.<br \/>\n2<sup>-x + 1<\/sup> = &#8211;\\(\\frac{3}{4}\\)x + 3<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n5<sup>x<\/sup> = -4<sup>-x + 4<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42847\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 33\" width=\"565\" height=\"247\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-33.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-33-300x131.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 34.<br \/>\n7<sup>x &#8211; 2<\/sup> = 2<sup>-x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n2<sup>-x &#8211; 3<\/sup> = 3<sup>x + 1<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42846\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 35\" width=\"297\" height=\"243\" \/><\/p>\n<p>Question 36.<br \/>\n5<sup>-2x + 3<\/sup> = -6<sup>x + 5<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 37\u201340, solve the equation by using the Property of Equality for Exponential Equations.<\/b><\/p>\n<p>Question 37.<br \/>\n30 \u2022 5<sup>x + 3<\/sup> = 150<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42845\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 37\" width=\"492\" height=\"306\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-37.png 492w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-37-300x187.png 300w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><\/p>\n<p>Question 38.<br \/>\n12 \u2022 2<sup>x &#8211; 7<\/sup> = 24<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n4(3<sup>-2x &#8211; 4<\/sup>) = 36<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 39\" width=\"465\" height=\"366\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-39.png 465w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-39-300x236.png 300w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/><\/p>\n<p>Question 40.<br \/>\n2(4<sup>2x + 1<\/sup>) = 128<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b><br \/>\nYou scan a photo into a computer at four times its original size. You continue to increase its size repeatedly by 100% using the computer. The new size of the photo y in comparison to its original size after x enlargements on the computer is represented by y = 2<sup>x + 2<\/sup>. How many times must the photo be enlarged on the computer so the new photo is 32 times the original size?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 41\" width=\"528\" height=\"296\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-41.png 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-41-300x168.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p>Question 42.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> A bacterial culture quadruples in size every hour. You begin observing the number of bacteria 3 hours after the culture is prepared. The amount y of bacteria x hours after the culture is prepared is represented by y = 192(4<sup>x &#8211; 3<\/sup>). When will there be 200,000 bacteria?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38340\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-105.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 105\" width=\"276\" height=\"191\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 43\u201346, solve the equation.<\/b><\/p>\n<p>Question 43.<br \/>\n3<sup>3x + 6<\/sup> = 27<sup>x + 2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42842\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 43\" width=\"512\" height=\"339\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-43.png 512w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-43-300x199.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/p>\n<p>Question 44.<br \/>\n3<sup>4x + 3<\/sup> = 81<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n4<sup>x + 3<\/sup> = 2<sup>2(x + 1)<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42841\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 45\" width=\"499\" height=\"333\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-45.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-45-300x200.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p>Question 46.<br \/>\n5<sup>8(x &#8211; 1)<\/sup> = 625<sup>2x &#8211; 2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<b>NUMBER SENSE<\/b><br \/>\nExplain how you can use mental math to solve the equation 8<sup>x &#8211; 4<\/sup> = 1.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42840\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 47\" width=\"537\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-47.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-47-300x35.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Question 48.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nThere are a total of 128 teams at the start of a citywide 3-on-3 basketball tournament. Half the teams are eliminated after each round. Write and solve an exponential equation to determine after which round there are 16 teams left.<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nYou deposit $500 in a savings account that earns 6% annual interest compounded yearly. Write and solve an exponential equation to determine when the balance of the account will be $800.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 49\" width=\"557\" height=\"509\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-49.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-49-300x274.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 50.<br \/>\n<b>HOW DO YOU SEE IT? <\/b>The graph shows the annual attendance at two different events. Each event began in 2004.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38341\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-106.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 106\" width=\"327\" height=\"235\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-106.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-106-300x216.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\na. Estimate when the events will have about the same attendance.<br \/>\nb. Explain how you can verify your answer in part(a).<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<b>REASONING<\/b><br \/>\nExplain why the Property of Equality for Exponential Equations does not work when b = 1. Give an example to justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42838\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 51\" width=\"582\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-51.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-51-300x32.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 52.<br \/>\n<b>THOUGHT PROVOKING<\/b><br \/>\nIs it possible for an exponential equation to have two different solutions? If not, explain your reasoning. If so, give an example.<br \/>\nAnswer:<\/p>\n<p><b>USING STRUCTURE<br \/>\nIn Exercises 53\u201358, solve the equation.<\/b><\/p>\n<p>Question 53.<br \/>\n8<sup>x &#8211; 2<\/sup> = \\(\\sqrt{8}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 53\" width=\"369\" height=\"286\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-53.png 369w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-53-300x233.png 300w\" sizes=\"(max-width: 369px) 100vw, 369px\" \/><\/p>\n<p>Question 54.<br \/>\n\\(\\sqrt{5}\\) = 5<sup>x + 4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n(\\(\\sqrt[5]{7}\\))<sup>x <\/sup>= 5<sup>2x + 3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 55\" width=\"477\" height=\"423\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-55.png 477w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-55-300x266.png 300w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><\/p>\n<p>Question 56.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38343\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-108.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 108\" width=\"139\" height=\"37\" \/><br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38344\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-109.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 109\" width=\"145\" height=\"39\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 57\" width=\"444\" height=\"497\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-57.png 444w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-57-268x300.png 268w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/p>\n<p>Question 58.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38345\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-110.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 110\" width=\"158\" height=\"45\" \/><br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n<b>MAKING AN ARGUMENT<\/b><br \/>\nConsider the equation (\\(\\frac{1}{a}\\))<sup>x<\/sup> = b, where a &gt; 1 and b &gt; 1. Your friend says the value of x will always be negative. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-59.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 59\" width=\"576\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-59.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-59-300x74.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Determine whether the sequence is arithmetic. If so, find the common difference.<\/b>(Section 4.6)<\/p>\n<p>Question 60.<br \/>\n-20, -26, -32, -38, . . .<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n9, 18, 36, 72, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-61.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 61\" width=\"578\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-61.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-61-300x93.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 62.<br \/>\n-5, -8, -12, -17, . . .<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n10, 20, 30, 40, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-63.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.5 Question 63\" width=\"558\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-63.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.5-Question-63-300x87.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<h3><a id=\"Lesson_6.6_Geometric_Sequences\"><\/a>Lesson 6.6 Geometric Sequences<\/h3>\n<p><b>Essential Question<\/b><\/p>\n<p>How can you use a geometric sequence to describe a pattern?<\/p>\n<p>In a geometric sequence, the ratio between each pair of consecutive terms is the same. This ratio is called the common ratio.<\/p>\n<p><b>EXPLORATION 1<br \/>\nDescribing Calculator Patterns<br \/>\nWork with a partner. <\/b>Enter the keystrokes on a calculator and record the results in the table. Describe the pattern.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38346\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-111.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 111\" width=\"590\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-111.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-111-300x144.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><br \/>\nc. Use a calculator to make your own sequence. Start with any number and multiply by 3 each time. Record your results in the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38347\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-112.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 112\" width=\"274\" height=\"89\" \/><br \/>\nd. Part (a) involves a geometric sequence with a common ratio of 2. What is the common ratio in part (b)? part (c)?<\/p>\n<p><b>EXPLORATION 2<br \/>\nFolding a Sheet of Paper<br \/>\nWork with a partner.<\/b> A sheet of paper is about 0.1 millimeter thick.<br \/>\na. How thick will it be when you fold it in half once? twice? three times?<br \/>\nb. What is the greatest number of times you can fold a piece of paper in half? How thick is the result?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38348\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-113.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 113\" width=\"262\" height=\"255\" \/><br \/>\nc. Do you agree with the statement below? Explain your reasoning.\u201cIf it were possible to fold the paper in half 15 times, it would be taller than you.\u201d<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-114.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 114\" width=\"175\" height=\"234\" \/><\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you use a geometric sequence to describe a pattern?<\/p>\n<p>Question 4.<br \/>\nGive an example of a geometric sequence from real life other than paper folding.<\/p>\n<p><b>6.6 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Decide whether the sequence is arithmetic, geometric, or neither. Explain your reasoning.<\/b><\/p>\n<p>Question 1.<br \/>\n5, 1, -3, -7, . . .<\/p>\n<p>Question 2.<br \/>\n1024, 128, 16, 2, . . .<\/p>\n<p>Question 3.<br \/>\n2, 6, 10, 16, . .<\/p>\n<p><b>Write the next three terms of the geometric sequence. Then graph the sequence.<\/b><\/p>\n<p>Question 4.<br \/>\n1, 3, 9, 27, . . .<\/p>\n<p>Question 5.<br \/>\n2500, 500, 100, 20, . . .<\/p>\n<p>Question 6.<br \/>\n80, -40, 20, -10, . . .<\/p>\n<p>Question 7.<br \/>\n-2, 4, -8, 16, . . .<\/p>\n<p><b>Write an equation for the nth term of the geometric sequence. Then find a<sub>7<\/sub>.<\/b><\/p>\n<p>Question 8.<br \/>\n1, -5, 25, -125, . . .<\/p>\n<p>Question 9.<br \/>\n13, 26, 52, 104, . . .<\/p>\n<p>Question 10.<br \/>\n432, 72, 12, 2, . . .<\/p>\n<p>Question 11.<br \/>\n4, 10, 25, 62.5, . . .<\/p>\n<p>Question 12.<br \/>\n<b>WHAT IF?<\/b> After how many clicks on the zoom-out button is the side length of the map 2560 miles?<\/p>\n<h3><a id=\"Geometric_Sequences_6.6_Exercises\"><\/a>Geometric Sequences 6.6 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>WRITING<\/b> Compare the two sequences.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38350\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-115.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 115\" width=\"289\" height=\"37\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 1\" width=\"571\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-1.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-1-300x46.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>CRITICAL THINKING<\/b> Why do the points of a geometric sequence lie on an exponential curve only when the common ratio is positive?<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 3\u20138, find the common ratio of the geometric sequence.<\/b><\/p>\n<p>Question 3.<br \/>\n4, 12, 36, 108, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42830\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 3\" width=\"496\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-3.png 496w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-3-300x108.png 300w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><\/p>\n<p>Question 4.<br \/>\n36, 6, 1, \\(\\frac{1}{6}\\), . . .<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{3}{8}\\), -3, 24, -192, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 5\" width=\"511\" height=\"256\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-5.png 511w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-5-300x150.png 300w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><\/p>\n<p>Question 6.<br \/>\n0.1, 1, 10, 100, . . .<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n128, 96, 72, 54, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 7\" width=\"501\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-7.png 501w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-7-300x122.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/p>\n<p>Question 8.<br \/>\n-162, 54, -18, 6, . . .<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 9\u201314, determine whether the sequence is arithmetic, geometric, or neither. Explain your reasoning.<\/b><\/p>\n<p>Question 9.<br \/>\n-8, 0, 8, 16, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 9\" width=\"560\" height=\"246\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-9.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-9-300x132.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 10.<br \/>\n-1, 4, -7, 10, . . .<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n9, 14, 20, 27, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 11\" width=\"579\" height=\"403\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-11.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-11-300x209.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 12.<br \/>\n\\(\\frac{3}{49}\\), \\(\\frac{3}{7}\\), 3, 21, . . .<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n192, 24, 3, \\(\\frac{3}{8}\\), , . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 13\" width=\"573\" height=\"341\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-13.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-13-300x179.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 14.<br \/>\n-25, -18, -11, -4, . . .<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 15\u201318, determine whether the graph represents an arithmetic sequence, a geometric sequence, or neither. Explain your reasoning.<\/b><\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-116.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 116\" width=\"166\" height=\"171\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 15\" width=\"568\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-15.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-15-300x131.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-117.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 117\" width=\"168\" height=\"170\" \/><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-118.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 118\" width=\"157\" height=\"178\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 17\" width=\"578\" height=\"415\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-17.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-17-300x215.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-119.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 119\" width=\"165\" height=\"169\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 19\u201324, write the next three terms of the geometric sequence. Then graph the sequence.<\/b><\/p>\n<p>Question 19.<br \/>\n5, 20, 80, 320, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 19\" width=\"572\" height=\"423\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-19.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-19-300x222.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 20.<br \/>\n-3, 12, -48, 192, . . .<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n81, -27, 9, -3, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42821\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 21\" width=\"572\" height=\"415\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-21.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-21-300x218.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 22.<br \/>\n-375, -75, -15, -3, . . .<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n32, 8, 2, \\(\\frac{1}{2}\\), . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42820\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 23\" width=\"581\" height=\"511\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-23.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-23-300x264.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 24.<br \/>\n\\(\\frac{16}{9}\\), \\(\\frac{8}{3}\\), 4, 6, . . .<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 25\u201332, write an equation for the nth term\ue04aof the geometric sequence. Then find a<sub>6<\/sub>.<\/b><\/p>\n<p>Question 25.<br \/>\n2, 8, 32, 128, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42819\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 25\" width=\"451\" height=\"224\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-25.png 451w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-25-300x149.png 300w\" sizes=\"(max-width: 451px) 100vw, 451px\" \/><\/p>\n<p>Question 26.<br \/>\n0.6, -3, 15, -75, . . .<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n&#8211;\\(\\frac{1}{8}\\), &#8211;\\(\\frac{1}{4}\\), &#8211;\\(\\frac{1}{2}\\), -1, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42818\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 27\" width=\"473\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-27.png 473w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-27-300x190.png 300w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><\/p>\n<p>Question 28.<br \/>\n0.1, 0.9, 8.1, 72.9, . . .<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38355\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-120.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 120\" width=\"288\" height=\"82\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 29\" width=\"568\" height=\"216\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-29.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-29-300x114.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-121.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 121\" width=\"252\" height=\"78\" \/><br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-122.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 122\" width=\"176\" height=\"164\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 31\" width=\"542\" height=\"228\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-31.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-31-300x126.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38357\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-122.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 122.1\" width=\"163\" height=\"168\" \/><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nA badminton tournament begins with 128 teams. After the first round, 64 teams remain. After the second round, 32 teams remain. How many teams remain after the third, fourth, and fifth rounds?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 33\" width=\"580\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-33.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-33-300x133.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 34.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nThe graphing calculator screen displays an area of 96 square units. After you zoom out once, the area is 384 square units. After you zoom out a second time, the area is 1536 square units. What is the screen area after you zoom out four times?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-123.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 123\" width=\"208\" height=\"156\" \/><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<b>ERROR ANALYSIS<\/b><br \/>\nDescribe and correct the error in writing the next three terms of the geometric sequence.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-124.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 124\" width=\"369\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-124.png 369w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-124-300x92.png 300w\" sizes=\"(max-width: 369px) 100vw, 369px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42814\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 35\" width=\"389\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-35.png 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-35-300x185.png 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<p>Question 36.<br \/>\n<b>ERROR ANALYSIS<\/b> Describe and correct the error in writing an equation for the nth term of the geometric sequence.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38361\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-125.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 125\" width=\"341\" height=\"158\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-125.png 341w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-125-300x139.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> The distance (in millimeters) traveled by a swinging pendulum decreases after each swing, as shown in the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-126.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 126\" width=\"368\" height=\"237\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-126.png 368w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-126-300x193.png 300w\" sizes=\"(max-width: 368px) 100vw, 368px\" \/><br \/>\na. Write a function that represents the distance the pendulum swings on its nth swing.<br \/>\nb. After how many swings is the distance 256 millimeters?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42811\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-37.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 37.1\" width=\"590\" height=\"359\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-37.1.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-37.1-300x183.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-37.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 37.2\" width=\"592\" height=\"569\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-37.2.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-37.2-300x288.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 38.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> You start a chain email and send it to six friends. The next day, each of your friends forwards the email to six people. The process continues for a few days.<br \/>\na. Write a function that represents the number of people who have received the email after n days.<br \/>\nb. After how many days will 1296 people have received the email?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-127.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 127\" width=\"201\" height=\"243\" \/><br \/>\nAnswer:<\/p>\n<p><b>MATHEMATICAL CONNECTIONS In Exercises 39 and 40, (a) write a function that represents the sequence of figures and (b) describe the 10th figure in the sequence.<\/b><\/p>\n<p>Question 39.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-128.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 128\" width=\"332\" height=\"105\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-128.png 332w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-128-300x95.png 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42809\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 39\" width=\"593\" height=\"487\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-39.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-39-300x246.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p>Question 40.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-129.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 129\" width=\"340\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-129.png 340w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-129-300x105.png 300w\" sizes=\"(max-width: 340px) 100vw, 340px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<b>REASONING<\/b> Write a sequence that represents the number of teams that have been eliminated in round n of the badminton tournament in Exercise 33. Determine whether the sequence is arithmetic, geometric, or neither. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42808\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 41\" width=\"577\" height=\"329\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-41.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-41-300x171.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 42.<br \/>\n<b>REASONING<\/b> Write a sequence that represents the perimeter of the graphing calculator screen in Exercise 34 after you zoom out n times. Determine whether the sequence is arithmetic, geometric, or neither. Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<b>WRITING<\/b> Compare the graphs of arithmetic sequences to the graphs of geometric sequences.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42807\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 43\" width=\"580\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-43.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-43-300x89.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 44.<br \/>\n<b>MAKING AN ARGUMENT<\/b> You are given two consecutive terms of a sequence.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38366\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-130.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 130\" width=\"121\" height=\"41\" \/><br \/>\nYour friend says that the sequence is not geometric. A classmate says that is impossible to know given only two terms. Who is correct? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<b>CRITICAL THINKING <\/b>Is the sequence shown an arithmetic sequence? a geometric sequence? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38367\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-131.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 131\" width=\"110\" height=\"32\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42806\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 45\" width=\"583\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-45.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-45-300x58.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 46.<br \/>\n<b>HOW DO YOU SEE IT? <\/b>Without performing any calculations, match each equation with its graph. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-132.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 132\" width=\"375\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-132.png 375w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-132-300x194.png 300w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<b>REASONING<\/b> What is the 9th term of the geometric sequence where a<sub>3<\/sub> = 81 and r = 3?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42805\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 47\" width=\"470\" height=\"274\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-47.png 470w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-47-300x175.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/p>\n<p>Question 48.<br \/>\n<b>OPEN-ENDED<\/b> Write a sequence that has a pattern but is not arithmetic or geometric. Describe the pattern.<\/p>\n<p>Question 49.<br \/>\n<b>ATTENDING TO PRECISION<\/b> Are the terms of a geometric sequence independent or dependent? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42804\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 49\" width=\"539\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-49.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-49-300x34.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 50.<br \/>\n<b>DRAWING CONCLUSIONS <\/b>A college student makes a deal with her parents to live at home instead of living on campus. She will pay her parents $0.01 for the first day of the month, $0.02 for the second day, $0.04 for the third day, and so on.<br \/>\na. Write an equation that represents the nth term of the geometric sequence.<br \/>\nb. What will she pay on the 25th day?<br \/>\nc. Did the student make a good choice or should she have chosen to live on campus? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<b>REPEATED REASONING<\/b> A soup kitchen makes 16 gallons of soup. Each day, a quarter of the soup is served and the rest is saved for the next day.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38369\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-133.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 133\" width=\"162\" height=\"196\" \/><br \/>\na. Write the first five terms of the sequence of the number of fluid ounces of soup left each day.<br \/>\nb. Write an equation that represents the nth term of the sequence.<br \/>\nc. When is all the soup gone? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-51.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 51.1\" width=\"615\" height=\"472\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-51.1.png 615w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-51.1-300x230.png 300w\" sizes=\"(max-width: 615px) 100vw, 615px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42802\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-51.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 51.2\" width=\"579\" height=\"439\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-51.2.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-51.2-300x227.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 52.<br \/>\n<b>THOUGHT PROVOKING<\/b> Find the sum of the terms of the geometric sequence.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-134.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 134\" width=\"185\" height=\"57\" \/><br \/>\nExplain your reasoning. Write a different infinite geometric sequence that has the same sum.<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<b>OPEN-ENDED<\/b> Write a geometric sequence in which a<sub>2<\/sub> &lt; a<sub>1<\/sub> &lt; a<sub>3<\/sub>.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42801\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 53\" width=\"312\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-53.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-53-300x32.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/p>\n<p>Question 54.<br \/>\n<b>NUMBER SENSE<\/b> Write an equation that represents the nth term of each geometric sequence shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38372\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-135.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 135\" width=\"281\" height=\"157\" \/><br \/>\na. Do the terms a<sub>1<\/sub> &#8211; b<sub>1<\/sub>, a<sub>2<\/sub> &#8211; b<sub>2<\/sub>, a<sub>3<\/sub> &#8211; b<sub>3<\/sub>, . . . form a geometric sequence? If so, how does the common ratio relate to the common ratios of the sequences above?<br \/>\nb. Do the terms <img loading=\"lazy\" class=\"alignnone size-full wp-image-38371\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-135.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 135.1\" width=\"99\" height=\"43\" \/> form a geometric sequence? If so, how does the common ratio relate to the common ratios of the sequences above?<br \/>\nAnswer:<\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Use residuals to determine whether the model is a good fit for the data in the table. Explain.<\/b><\/p>\n<p>Question 55.<br \/>\ny = 3x &#8211; 8<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38373\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-136.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 136\" width=\"363\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-136.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-136-300x64.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-55.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 55.1\" width=\"568\" height=\"371\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-55.1.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-55.1-300x196.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42799\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-55.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.6 Question 55.2\" width=\"574\" height=\"318\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-55.2.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.6-Question-55.2-300x166.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 56.<br \/>\ny = -5x + 1<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38374\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-137.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 137\" width=\"359\" height=\"76\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-137.png 359w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-137-300x64.png 300w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_6.7_Recursively_Defined_Sequences\"><\/a>Lesson 6.7 Recursively Defined Sequences<\/h3>\n<p><b>Essential Question<\/b><\/p>\n<p>How can you define a sequence recursively?<br \/>\nA recursive rule gives the beginning term(s) of a sequence and a recursive equation that tells how a<sub>n<\/sub> is related to one or more preceding terms.<\/p>\n<p><b>EXPLORATION 1<br \/>\nDescribing a Pattern<br \/>\nWork with a partner.<\/b> Consider a hypothetical population of rabbits. Start with one breeding pair. After each month, each breeding pair produces another breeding pair. The total number of rabbits each month follows the exponential pattern 2, 4, 8, 16, 32,. . .. Now suppose that in the first month after each pair is born, the pair is too young to reproduce. Each pair produces another pair after it is 2 months old. Find the total number of pairs in months 6, 7, and 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38375\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-138.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 138\" width=\"571\" height=\"367\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-138.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-138-300x193.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p><b>EXPLORATION 2<br \/>\nUsing a Recursive Equation<br \/>\nWork with a partner.<\/b> Consider the following recursive equation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38377\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-139.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 139\" width=\"434\" height=\"170\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-139.png 434w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-139-300x118.png 300w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><br \/>\nEach term in the sequence is the sum of the two preceding terms.<br \/>\nCopy and complete the table. Compare the results with the sequence of the number of pairs in Exploration 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38376\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-139.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 139.1\" width=\"495\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-139.1.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-139.1-300x53.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you define a sequence recursively?<\/p>\n<p>Question 4.<br \/>\nUse the Internet or some other reference to determine the mathematician who first described the sequences in Explorations 1 and 2.<\/p>\n<p><b>6.7 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Write a recursive rule for the sequence.<\/b><\/p>\n<p>Question 5.<br \/>\n8, 3, -2, -7, -12, . . .<\/p>\n<p>Question 6.<br \/>\n1.3, 2.6, 3.9, 5.2, 6.5, . . .<\/p>\n<p>Question 7.<br \/>\n4, 20, 100, 500, 2500, . . .<\/p>\n<p>Question 8.<br \/>\n128, -32, 8, -2, 0.5, . . .<\/p>\n<p>Question 9.<br \/>\nWrite a recursive rule for the height of the sunflower over time.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38378\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-140.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 140\" width=\"474\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-140.png 474w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-140-300x72.png 300w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Write an explicit rule for the recursive rule.<\/b><\/p>\n<p>Question 10.<br \/>\na<sub>1<\/sub> = -45, a<sub>n<\/sub> = a<sub>n &#8211; 1<\/sub> + 20<\/p>\n<p>Question 11.<br \/>\na<sub>1<\/sub> = 13, a<sub>n<\/sub> = -3a<sub>n &#8211; 1<\/sub><\/p>\n<p><b>Write a recursive rule for the explicit rule.<\/b><\/p>\n<p>Question 12.<br \/>\na<sub>n<\/sub> = -n + 1<\/p>\n<p>Question 13.<br \/>\na<sub>n<\/sub> = -2.5(4)<sub>n &#8211; 1<\/sub><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Write a recursive rule for the sequence. Then write the next three terms of the sequence.<\/b><\/p>\n<p>Question 14.<br \/>\n5, 6, 11, 17, 28, . . .<\/p>\n<p>Question 15.<br \/>\n-3, -4, -7, -11, -18, . . .<\/p>\n<p>Question 16.<br \/>\n1, 1, 0, -1, -1, 0, 1, 1, . . .<\/p>\n<p>Question 17.<br \/>\n4, 3, 1, 2, -1, 3, -4, . . .<\/p>\n<h3><a id=\"Recursively_Defined_Sequences_6.7_Exercises\"><\/a>Recursively Defined Sequences 6.7 Exercises<\/h3>\n<p>Question 1.<br \/>\n<b>COMPLETE THE SENTENCE<\/b> A recursive rule gives the beginning term(s) of a sequence and a(n)_____________ that tells how a<sub>n<\/sub> is related to one or more preceding terms.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42798\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 1\" width=\"579\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-1.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-1-300x45.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>WHICH ONE DOESN\u2019T BELONG?<\/b> Which rule does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38379\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-141.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 141\" width=\"687\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-141.png 687w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-141-300x28.png 300w\" sizes=\"(max-width: 687px) 100vw, 687px\" \/><br \/>\nAnswer:<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p><b>In Exercises 3\u20136, determine whether the recursive rule represents an arithmetic sequence or a geometric sequence.<\/b><\/p>\n<p>Question 3.<br \/>\na<sub>1<\/sub> = 2, a<sub>n<\/sub> = 7a<sub>n &#8211; 1<\/sub><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42797\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 3\" width=\"501\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-3.png 501w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-3-300x37.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/p>\n<p>Question 4.<br \/>\na<sub>1<\/sub> = 18, a<sub>n<\/sub> = a<sub>n &#8211; 1<\/sub> + 1<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\na<sub>1<\/sub> = 5, a<sub>n<\/sub> = a<sub>n &#8211; 1<\/sub> &#8211; 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42796\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 5\" width=\"534\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-5.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-5-300x34.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Question 6.<br \/>\na<sub>1<\/sub> = 3, a<sub>n<\/sub> = -6a<sub>n &#8211; 1<\/sub><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 7\u201312, write the first six terms of the sequence. Then graph the sequence.<\/b><\/p>\n<p>Question 7.<br \/>\na<sub>1<\/sub> = 0, a<sub>n<\/sub> = a<sub>n &#8211; 1<\/sub> + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42795\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 7\" width=\"541\" height=\"498\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-7.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-7-300x276.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 8.<br \/>\na<sub>1<\/sub> = 10, a<sub>n<\/sub> = a<sub>n &#8211; 1<\/sub> &#8211; 5<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\na<sub>1<\/sub> = 2, a<sub>n<\/sub> = 3a<sub>n &#8211; 1<\/sub><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42794\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 9\" width=\"521\" height=\"530\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-9.png 521w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-9-295x300.png 295w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><\/p>\n<p>Question 10.<br \/>\na<sub>1<\/sub> = 8, a<sub>n<\/sub> = 1.5a<sub>n &#8211; 1<\/sub><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\na<sub>1<\/sub> = 80, a<sub>n<\/sub> = &#8211;\\(\\frac{1}{2}\\)a<sub>n &#8211; 1<\/sub><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42793\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 11\" width=\"652\" height=\"572\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-11.png 652w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-11-300x263.png 300w\" sizes=\"(max-width: 652px) 100vw, 652px\" \/><\/p>\n<p>Question 12.<br \/>\na<sub>1<\/sub> = -7, a<sub>n<\/sub> = -4a<sub>n &#8211; 1<\/sub><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 13\u201320, write a recursive rule for the sequence.<\/b><\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38380\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-142.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 142\" width=\"286\" height=\"75\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42792\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 13\" width=\"597\" height=\"289\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-13.png 597w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-13-300x145.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38381\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-143.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 143\" width=\"255\" height=\"79\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n243, 81, 27, 9, 3, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42791\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 15\" width=\"583\" height=\"339\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-15.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-15-300x174.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 16.<br \/>\n3, 11, 19, 27, 35, . . .<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n0, -3, -6, -9, -12, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42790\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 17\" width=\"578\" height=\"336\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-17.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-17-300x174.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 18.<br \/>\n5, -20, 80, -320, 1280, . . .<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38382\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-144.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 144\" width=\"167\" height=\"164\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42789\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 19\" width=\"556\" height=\"297\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-19.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-19-300x160.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-145.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 145\" width=\"164\" height=\"175\" \/><br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>Write a recursive rule for the number of bacterial cells over time.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38384\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-146.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 146\" width=\"327\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-146.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-146-300x175.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42788\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 21\" width=\"594\" height=\"322\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-21.png 594w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-21-300x163.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p>Question 22.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> Write a recursive rule for the length of the deer antler over time.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38385\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-147.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 147\" width=\"319\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-147.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-147-300x151.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 23\u201328, write an explicit rule for the recursive rule.<\/b><\/p>\n<p>Question 23.<br \/>\na<sub>1<\/sub> = -3, a<sub>n<\/sub> = a<sub>n &#8211; 1<\/sub> + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42787\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 23\" width=\"588\" height=\"270\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-23.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-23-300x138.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 24.<br \/>\na<sub>1<\/sub> = 8, a<sub>n<\/sub> = a<sub>n &#8211; 1<\/sub> &#8211; 12<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\na<sub>1<\/sub> = 16, a<sub>n<\/sub> = 0.5a<sub>n &#8211; 1<\/sub><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42786\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 25\" width=\"574\" height=\"168\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-25.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-25-300x88.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 26.<br \/>\na<sub>1<\/sub> = -2, a<sub>n<\/sub> = 9a<sub>n &#8211; 1<\/sub><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\na<sub>1<\/sub> = 4, a<sub>n<\/sub> = a<sub>n &#8211; 1<\/sub> + 17<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42785\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 27\" width=\"599\" height=\"273\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-27.png 599w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-27-300x137.png 300w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><\/p>\n<p>Question 28.<br \/>\na<sub>1<\/sub> = 5, a<sub>n<\/sub> = -5a<sub>n &#8211; 1<\/sub><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 29\u201334, write a recursive rule for the explicit rule.<\/b><\/p>\n<p>Question 29.<br \/>\na<sub>n<\/sub> = 7(3)<sup>n &#8211; 1<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42784\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 29\" width=\"555\" height=\"170\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-29.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-29-300x92.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 30.<br \/>\na<sub>n<\/sub> = -4n + 2<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\na<sub>n<\/sub> = 1.5n + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42783\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 31\" width=\"576\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-31.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-31-300x106.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 32.<br \/>\na<sub>n<\/sub> = 6n &#8211; 20<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\na<sub>n<\/sub> = (-5)<sup>n &#8211; 1<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42782\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 33\" width=\"565\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-33.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-33-300x91.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 34.<br \/>\na<sub>n<\/sub> = -81(\\(\\frac{2}{3}\\))<sup>n &#8211; 1<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 35\u201338, graph the first four terms of the sequence with the given description. Write a recursive rule and an explicit rule for the sequence.<\/b><\/p>\n<p>Question 35.<br \/>\nThe first term of a sequence is 5. Each term of the sequence is 15 more than the preceding term.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42781\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-35.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 35.1\" width=\"563\" height=\"620\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-35.1.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-35.1-272x300.png 272w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 36.<br \/>\nThe first term of a sequence is 16. Each term of the sequence is half the preceding term.<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\nThe first term of a sequence is -1. Each term of the sequence is -3 times the preceding term.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42780\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 37\" width=\"556\" height=\"524\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-37.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-37-300x283.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 38.<br \/>\nThe first term of a sequence is 19. Each term of the sequence is 13 less than the preceding term.<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 39\u201344, write a recursive rule for the sequence. Then write the next two terms of the sequence.<\/b><\/p>\n<p>Question 39.<br \/>\n1, 3, 4, 7, 11, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42779\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 39\" width=\"586\" height=\"374\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-39.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-39-300x191.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 40.<br \/>\n10, 9, 1, 8, -7, 15, . . .<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n2, 4, 2, -2, -4, -2, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 41\" width=\"568\" height=\"397\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-41.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-41-300x210.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 42.<br \/>\n6, 1, 7, 8, 15, 23, . . .<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38386\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-148.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 148\" width=\"157\" height=\"176\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42777\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 43\" width=\"591\" height=\"360\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-43.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-43-300x183.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p>Question 44.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38387\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-149.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 149\" width=\"167\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-149.png 167w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-149-150x150.png 150w\" sizes=\"(max-width: 167px) 100vw, 167px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<b>ERROR ANALYSIS<\/b> Describe and correct the error in writing an explicit rule for the recursive rule a<sub>1<\/sub> = 6, a<sub>n<\/sub> = a<sub>n &#8211; 1<\/sub> &#8211; 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38388\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-150.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 150\" width=\"311\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-150.png 311w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-150-300x127.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42776\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 45\" width=\"535\" height=\"298\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-45.png 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-45-300x167.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p>Question 46.<br \/>\n<b>ERROR ANALYSIS<\/b> Describe and correct the error in writing a recursive rule for the sequence 2, 4, 6, 10, 16, . . ..<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38389\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-151.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 151\" width=\"356\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-151.png 356w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-151-300x158.png 300w\" sizes=\"(max-width: 356px) 100vw, 356px\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 47\u201351, the function f represents a sequence. Find the 2nd, 5th, and 10th terms of the sequence.<\/b><\/p>\n<p>Question 47.<br \/>\nf(1) = 3, f (n) = f(n &#8211; 1) + 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42775\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 47\" width=\"595\" height=\"404\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-47.png 595w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-47-300x204.png 300w\" sizes=\"(max-width: 595px) 100vw, 595px\" \/><\/p>\n<p>Question 48.<br \/>\nf(1) = -1, f(n) = 6f(n &#8211; 1)<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\nf(1) = 8, f(n) = -f(n &#8211; 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42774\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 49\" width=\"573\" height=\"304\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-49.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-49-300x159.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 50.<br \/>\nf(1) = 4, f(2) = 5, f(n) = f(n &#8211; 2) + f(n &#8211; 1)<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\nf(1) = 10, f(2) = 15, f(n) = f(n &#8211; 1) &#8211; f(n &#8211; 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42773\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 51\" width=\"566\" height=\"404\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-51.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-51-300x214.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 52.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>The X-ray shows the lengths (in centimeters) of bones in a human hand.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38390\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-152.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 152\" width=\"245\" height=\"174\" \/><br \/>\na. Write a recursive rule for the lengths of the bones.<br \/>\nb. Measure the lengths of different sections of your hand. Can the lengths be represented by a recursively defined sequence? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<b>USING TOOLS<\/b> You can use a spreadsheet to generate the terms of a sequence.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38391\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-153.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 153\" width=\"330\" height=\"159\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-153.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-153-300x145.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\na. To generate the terms of the sequence a<sub>1<\/sub> = 3, a<sub>n<\/sub> = a<sub>n &#8211; 1<\/sub> + 2, enter the value of a<sub>1<\/sub>, 3, into cell A1. Then enter \u201c=A1+2\u201d into cell A2, as shown. Use the fill down feature to generate the first 10 terms of the sequence.<br \/>\nb. Use a spreadsheet to generate the first 10 terms of the sequence a<sub>1<\/sub> = 3, a<sub>n<\/sub> = 4a<sub>n &#8211; 1<\/sub>. (Hint: Enter \u201c=4*A1\u201d into cell A2.)<br \/>\nc. Use a spreadsheet to generate the first 10 terms of the sequence a<sub>1<\/sub> = 4, a<sub>2<\/sub> = 7, a<sub>n<\/sub> = a<sub>n &#8211; 1<\/sub> &#8211; a<sub>n &#8211; 2<\/sub>. (Hint: Enter \u201c=A2-A1\u201d into cell A3.)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42772\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-53.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 53.1\" width=\"603\" height=\"409\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-53.1.png 603w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-53.1-300x203.png 300w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42771\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-53.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 53.2\" width=\"615\" height=\"405\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-53.2.png 615w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-53.2-300x198.png 300w\" sizes=\"(max-width: 615px) 100vw, 615px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42770\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-53.3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 53.3\" width=\"664\" height=\"424\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-53.3.png 664w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-53.3-300x192.png 300w\" sizes=\"(max-width: 664px) 100vw, 664px\" \/><\/p>\n<p>Question 54.<br \/>\n<b>HOW DO YOU SEE IT? <\/b>Consider Squares 1\u20136 in the diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-154.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 154\" width=\"283\" height=\"175\" \/><br \/>\na. Write a sequence in which each term an is the side length of square n.<br \/>\nb. What is the name of this sequence? What is the next term of this sequence?<br \/>\nc. Use the term in part (b) to add another square to the diagram and extend the spiral.<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<b>REASONING<\/b> Write the first 5 terms of the sequence a<sub>1<\/sub> = 5, a<sub>n<\/sub> = 3a<sub>n &#8211; 1<\/sub> + 4. Determine whether the sequence is arithmetic, geometric, or neither. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42769\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 55\" width=\"629\" height=\"537\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-55.png 629w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-55-300x256.png 300w\" sizes=\"(max-width: 629px) 100vw, 629px\" \/><\/p>\n<p>Question 56.<br \/>\n<b>THOUGHT PROVOKING<\/b> Describe the pattern for the numbers in Pascal\u2019s Triangle, shown below. Write a recursive rule that gives the mth number in the nth row.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38393\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-155.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 155\" width=\"194\" height=\"131\" \/><br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<b>REASONING<\/b> The explicit rule a<sub>n<\/sub> = a<sub>1<\/sub> + (n &#8211; 1)d defines an arithmetic sequence.<br \/>\na. Explain why a<sub>n &#8211; 1<\/sub> = a<sub>1<\/sub> + [(n &#8211; 1) &#8211; 1]d.<br \/>\nb. Justify each step in showing that a recursive equation for the sequence is a<sub>n<\/sub> = a<sub>n &#8211; 1<\/sub> + d.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38394\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-156.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 156\" width=\"352\" height=\"192\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-156.png 352w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-156-300x164.png 300w\" sizes=\"(max-width: 352px) 100vw, 352px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42768\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 57\" width=\"592\" height=\"354\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-57.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-57-300x179.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 58.<br \/>\n<b>MAKING AN ARGUMENT<\/b> Your friend claims that the sequence<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-157.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 157\" width=\"162\" height=\"39\" \/><br \/>\ncannot be represented by a recursive rule. Is your friend correct? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n<b>PROBLEM SOLVING <\/b>Write a recursive rule for the sequence.<br \/>\n3, 7, 15, 31, 63, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42767\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-59.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 59\" width=\"586\" height=\"186\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-59.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-59-300x95.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Simplify the expression.<\/b><\/p>\n<p>Question 60.<br \/>\n5x + 12x<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n9 &#8211; 6y &#8211; 14<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42766\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-61.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 61\" width=\"296\" height=\"68\" \/><\/p>\n<p>Question 62.<br \/>\n2d &#8211; 7 &#8211; 8d<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n3 &#8211; 3m + 11m<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42765\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-63.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 63\" width=\"318\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-63.png 318w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-63-300x58.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><\/p>\n<p><b>Write a linear function f with the given values<\/b>.(Section 4.2)<\/p>\n<p>Question 64.<br \/>\nf(2) = 6, f(-1) = -3<br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\nf (-2) = 0, f(6) = -4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42764\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-65.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 65\" width=\"446\" height=\"320\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-65.png 446w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-65-300x215.png 300w\" sizes=\"(max-width: 446px) 100vw, 446px\" \/><\/p>\n<p>Question 66.<br \/>\nf(-3) = 5, f(-1) = 5<br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\nf(3) = -1, f(-4) = -15<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42763\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-67.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences 6.7 Question 67\" width=\"492\" height=\"299\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-67.png 492w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences-6.7-Question-67-300x182.png 300w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><\/p>\n<h3><a id=\"Exponential_Functions_and_Sequences_Performance_Task:_The_New_Car\"><\/a>Exponential Functions and Sequences Performance Task: The New Car<\/h3>\n<p><b>6.5\u20136.7<\/b><\/p>\n<p><b>Core Vocabulary<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38396\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-158.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 158\" width=\"665\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-158.png 665w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-158-300x26.png 300w\" sizes=\"(max-width: 665px) 100vw, 665px\" \/><\/p>\n<p><b>Core Concepts<br \/>\nSection 6.5<\/b><br \/>\nProperty of Equality for Exponential Equations, p. 326<br \/>\nSolving Exponential Equations by Graphing, p. 328<\/p>\n<p><b>Section 6.6<\/b><br \/>\nGeometric Sequence, p. 332<br \/>\nEquation for a Geometric Sequence, p. 334<\/p>\n<p><b>Section 6.7<\/b><br \/>\nRecursive Equation for an Arithmetic Sequence, p. 340<br \/>\nRecursive Equation for a Geometric Sequence, p. 340<\/p>\n<p><b>Mathematical Practices<\/b><\/p>\n<p>Question 1.<br \/>\nHow did you decide on an appropriate level of precision for your answer in Exercise 49 on page 330?<\/p>\n<p>Question 2.<br \/>\nExplain how writing a function in Exercise 39 part (a) on page 337 created a shortcut for answering part (b).<\/p>\n<p>Question 3.<br \/>\nHow did you choose an appropriate tool in Exercise 52 part (b) on page 345?<\/p>\n<p><b>Performance Task<\/b><\/p>\n<p><b>The New Car<\/b><\/p>\n<p>There is so much more to buying a new car than the purchase price. Interest rates, depreciation, and inflation are all factors. So, what is the real cost of your new car?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38397\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-159.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 159\" width=\"370\" height=\"373\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-159.png 370w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-159-298x300.png 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-159-150x150.png 150w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><br \/>\nTo explore the answers to this question and more, go to <img loading=\"lazy\" class=\"alignnone size-full wp-image-38399\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-160.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 160\" width=\"92\" height=\"85\" \/><\/p>\n<h3><a id=\"Exponential_Functions_and_Sequences_Chapter_Review\"><\/a>Exponential Functions and Sequences Chapter Review<\/h3>\n<p>Simplify the expression. Write your answer using only positive exponents.<\/p>\n<p>Question 1.<br \/>\ny<sup>3<\/sup> \u2022 y<sup>-5<\/sup><\/p>\n<p>Question 2.<br \/>\n\\(\\frac{x^{4}}{x^{7}}\\)<\/p>\n<p>Question 3.<br \/>\n(x<sup>0<\/sup>y<sup>2<\/sup>)<sup>3<\/sup><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-160.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 160.1\" width=\"70\" height=\"55\" \/><\/p>\n<p><b>Evaluate the expression.<\/b><\/p>\n<p>Question 5.<br \/>\n\\(\\sqrt[3]{8}\\)<\/p>\n<p>Question 6.<br \/>\n\\(\\sqrt[5]{-243}\\)<\/p>\n<p>Question 7.<br \/>\n625<sup>3 \/ 4<\/sup><\/p>\n<p>Question 8.<br \/>\n(-25)<sup>1 \/ 2<\/sup><\/p>\n<p>Question 9.<br \/>\nf(x) = -4 (\\(\\sqrt[1]{4}\\))<sup>x<\/sup><\/p>\n<p>Question 10.<br \/>\nf(x) = 3<sup>x + 2<\/sup><\/p>\n<p>Question 11.<br \/>\nf(x) = 2<sup>x &#8211; 4<\/sup> &#8211; 3<\/p>\n<p>Question 12.<br \/>\nWrite and graph an exponential function f represented by the table. Then compare the graph to the graph of g(x) = (\\(\\frac{1}{2}\\))<sup>x<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38400\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-161.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 161\" width=\"263\" height=\"75\" \/><\/p>\n<p><b>Determine whether the table represents an exponential growth function, an exponential decay function, or neither. Explain.<\/b><\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38401\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-162.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 162\" width=\"259\" height=\"81\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38402\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-163.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 163\" width=\"251\" height=\"79\" \/><\/p>\n<p><b>Rewrite the function to determine whether it represents exponential growth or exponential decay. Identify the percent rate of change.<\/b><\/p>\n<p>Question 15.<br \/>\nf(t) = 4(1.25)<sup>t + 3<\/sup><\/p>\n<p>Question 16.<br \/>\ny = (1.06)<sup>8t<\/sup><\/p>\n<p>Question 17.<br \/>\nf(t) = 6(0.84)<sup>t &#8211; 4<\/sup><\/p>\n<p>Question 18.<br \/>\nYou deposit $750 in a savings account that earns 5% annual interest compounded quarterly.<br \/>\n(a) Write a function that represents the balance after t years.<br \/>\n(b) What is the balance of the account after 4 years?<\/p>\n<p>Question 19.<br \/>\nThe value of a TV is $1500. Its value decreases by 14% each year.<br \/>\n(a) Write a function that represents the value y (in dollars) of the TV after t years.<br \/>\n(b) Find the approximate monthly percent decrease in value.<br \/>\n(c) Graph the function from part (a). Use the graph to estimate the value of the TV after 3 years.<\/p>\n<p><b>Solve the equation.<\/b><\/p>\n<p>Question 20.<br \/>\n5<sup>x<\/sup> = 5<sup>3x &#8211; 2<\/sup><\/p>\n<p>Question 21.<br \/>\n3<sup>x &#8211; 2<\/sup> = 1<\/p>\n<p>Question 22.<br \/>\n-4 = 6<sup>4x &#8211; 3<\/sup><\/p>\n<p>Question 23.<br \/>\n(\\(\\frac{1}{3}\\))<sup>2x + 3<\/sup> = 5<\/p>\n<p>Question 24.<br \/>\n(\\(\\frac{1}{16}\\))<sup>3x<\/sup> = 64<sup>2(x + 8)<\/sup><\/p>\n<p>Question 25.<br \/>\n27<sup>2x + 2<\/sup> = 81<sup>x + 4<\/sup><\/p>\n<p><b>Decide whether the sequence is arithmetic, geometric, or neither. Explain your reasoning. If the sequence is geometric, write the next three terms and graph the sequence.<\/b><\/p>\n<p>Question 26.<br \/>\n3, 12, 48, 192, . . .<\/p>\n<p>Question 27.<br \/>\n9, -18, 27, -36, . . .<\/p>\n<p>Question 28.<br \/>\n375, -75, 15, -3, . . .<\/p>\n<p><b>Write an equation for the nth term of the geometric sequence. Then find a<sub>9<\/sub>.<\/b><\/p>\n<p>Question 29.<br \/>\n1, 4, 16, 64, . . .<\/p>\n<p>Question 30.<br \/>\n5, -10, 20, -40, . . .<\/p>\n<p>Question 31.<br \/>\n486, 162, 54, 18, . . .<\/p>\n<p><b>Write the first six terms of the sequence. Then graph the sequence.<\/b><\/p>\n<p>Question 32.<br \/>\na<sub>1<\/sub> = 4, a<sub>n<\/sub> = a<sub>n &#8211; 1<\/sub> + 5<\/p>\n<p>Question 33.<br \/>\na<sub>1<\/sub> = -4, a<sub>n<\/sub> = -3a<sub>n &#8211; 1<\/sub><\/p>\n<p>Question 34.<br \/>\na<sub>1<\/sub> = 32, a<sub>n<\/sub> = \\(\\frac{1}{4}\\)a<sub>n \u2212 1<\/sub><\/p>\n<p><b>Write a recursive rule for the sequence.<\/b><\/p>\n<p>Question 35.<br \/>\n3, 8, 13, 18, 23, . . .<\/p>\n<p>Question 36.<br \/>\n3, 6, 12, 24, 48, . . .<\/p>\n<p>Question 37.<br \/>\n7, 6, 13, 19, 32, . .<\/p>\n<p>Question 38.<br \/>\nThe first term of a sequence is 8. Each term of the sequence is 5 times the preceding term. Graph the first four terms of the sequence. Write a recursive rule and an explicit rule for the sequence.<\/p>\n<h3><a id=\"Exponential_Functions_and_Sequences_Chapter_Test\"><\/a>Exponential Functions and Sequences Chapter Test<\/h3>\n<p><b>Evaluate the expression.<\/b><\/p>\n<p>Question 1.<br \/>\n&#8211;\\(\\sqrt[4]{16}\\)<\/p>\n<p>Question 2.<br \/>\n729\\(1 \/ 6\\)<\/p>\n<p>Question 3.<br \/>\n(-32)\\(7 \/ 5\\)<\/p>\n<p><b>Simplify the expression. Write your answer using only positive exponents.<\/b><\/p>\n<p>Question 4.<br \/>\nz<sup>-2<\/sup> \u2022 z<sup>4<\/sup><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38403\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-164.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 6 Exponential Functions and Sequences 164\" width=\"58\" height=\"44\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38281\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-165.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 6 Exponential Functions and Sequences 165\" width=\"71\" height=\"61\" \/><\/p>\n<p><b>Write and graph a function that represents the situation.<\/b><\/p>\n<p>Question 7.<br \/>\nYour starting annual salary of $42,500 increases by 3% each year.<\/p>\n<p>Question 8.<br \/>\nYou deposit $500 in an account that earns 6.5% annual interest compounded yearly.<\/p>\n<p><b>Write an explicit rule and a recursive rule for the sequence.<\/b><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38282\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-166.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 6 Exponential Functions and Sequences 166\" width=\"257\" height=\"75\" \/><\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38283\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-167.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 6 Exponential Functions and Sequences 167\" width=\"260\" height=\"79\" \/><\/p>\n<p><b>Solve the equation. Check your solution.<\/b><\/p>\n<p>Question 11.<br \/>\n2<sup>x<\/sup> = \\(\\frac{1}{128}\\)<\/p>\n<p>Question 12.<br \/>\n256<sup>x + 2<\/sup> = 16<sup>3x &#8211; 1<\/sup><\/p>\n<p>Question 13.<br \/>\nGraph f(x) = 2(6)<sup>x<\/sup>. Compare the graph to the graph of g(x) = 6<sup>x<\/sup>. Describe the domain and range of f.<\/p>\n<p><b>Use the equation to complete the statement <img loading=\"lazy\" class=\"alignnone size-full wp-image-38287\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-168.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 6 Exponential Functions and Sequences 168.3\" width=\"64\" height=\"30\" \/> with the symbol &lt; , &gt; , or =. Do not attempt to solve the equation.<\/b><\/p>\n<p>Question 14.<br \/>\n\\(\\frac{5^{a}}{5^{b}}\\)<\/p>\n<p>Question 15.<br \/>\n9<sup>a<\/sup> \u2022 9<sup>-b<\/sup><\/p>\n<p>Question 16.<br \/>\nThe first two terms of a sequence are a<sub>1<\/sub> = 3 and a<sub>2<\/sub> = -12. Let a<sub>3<\/sub> be the third term when the sequence is arithmetic and let b<sub>3<\/sub> be the third term when the sequence is geometric. Find a<sub>3<\/sub> &#8211; b<sub>3<\/sub>.<\/p>\n<p>Question 17.<br \/>\nAt sea level, Earth\u2019s atmosphere exerts a pressure of 1 atmosphere. Atmospheric pressure P (in atmospheres) decreases with altitude. It can be modeled by P =(0.99988)<sup>a<\/sup>, where a is the altitude (in meters).<br \/>\na. Identify the initial amount, decay factor, and decay rate.<br \/>\nb. Use a graphing calculator to graph the function. Use the graph to estimate the atmospheric pressure at an altitude of 5000 feet.<\/p>\n<p>Question 18.<br \/>\nYou follow the training schedule from your coach.<br \/>\na. Write an explicit rule and a recursive rule for the geometric sequence.<br \/>\nb. On what day do you run approximately 3 kilometers?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38284\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-168.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 6 Exponential Functions and Sequences 168.1\" width=\"325\" height=\"178\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-168.1.png 325w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-168.1-300x164.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><\/p>\n<h3><a id=\"Exponential_Functions_and_Sequences_Cumulative_Assessment\"><\/a>Exponential Functions and Sequences Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nFill in the exponent of x with a number to simplify the expression.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38285\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-168.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 6 Exponential Functions and Sequences 168.2\" width=\"181\" height=\"62\" \/><\/p>\n<p>Question 2.<br \/>\nThe graph of the exponential function f is shown. Find f(-7).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38286\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-168.3.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 6 Exponential Functions and Sequences 168.3\" width=\"193\" height=\"182\" \/><\/p>\n<p>Question 3.<br \/>\nStudent A claims he can form a linear system from the equations shown that has infinitely many solutions. Student B claims she can form a linear system from the equations shown that has one solution. Student C claims he can form a linear system from the equations shown that has no solution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-169.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 6 Exponential Functions and Sequences 169\" width=\"472\" height=\"124\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-169.png 472w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-169-300x79.png 300w\" sizes=\"(max-width: 472px) 100vw, 472px\" \/><br \/>\na. Select two equations to support Student A\u2019s claim.<br \/>\nb. Select two equations to support Student B\u2019s claim.<br \/>\nc. Select two equations to support Student C\u2019s claim.<\/p>\n<p>Question 4.<br \/>\nFill in the inequality with &lt; , \u2264 , &gt; , or \u2265 so that the system of linear inequalities has no solution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38289\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-170.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 6 Exponential Functions and Sequences 170\" width=\"248\" height=\"70\" \/><\/p>\n<p>Question 5.<br \/>\nThe second term of a sequence is 7. Each term of the sequence is 10 more than the preceding term. Fill in values to write a recursive rule and an explicit rule for the sequence.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38290\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-171.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 6 Exponential Functions and Sequences 171\" width=\"226\" height=\"87\" \/><\/p>\n<p>Question 6.<br \/>\nA data set consists of the heights y (in feet) of a hot-air balloon t minutes after it begins its descent. An equation of the line of best fit is y = 870 &#8211; 14.8t. Which of the following is a correct interpretation of the line of best fit?<br \/>\nA. The initial height of the hot-air balloon is 870 feet. The slope has no meaning in this context.<br \/>\nB. The initial height of the hot-air balloon is 870 feet, and it descends 14.8 feet per minute.<br \/>\nC. The initial height of the hot-air balloon is 870 feet, and it ascends 14.8 feet per minute.<br \/>\nD. The hot-air balloon descends 14.8 feet per minute. The y-intercept has no meaning in this context.<\/p>\n<p>Question 7.<br \/>\nSelect all the functions whose x-value is an integer when f(x) = 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38291\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-172.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 6 Exponential Functions and Sequences 172\" width=\"477\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-172.png 477w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-172-300x77.png 300w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><\/p>\n<p>Question 8.<br \/>\nPlace each function into one of the three categories. For exponential functions, state whether the function represents exponential growth, exponential decay, or neither.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-173.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 6 Exponential Functions and Sequences 173\" width=\"570\" height=\"262\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-173.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-173-300x138.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 9.<br \/>\nHow does the graph shown compare to the graph of f(x) = 2<sup>x<\/sup>?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38293\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-6-Exponential-Functions-and-Sequences-174.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 6 Exponential Functions and Sequences 174\" width=\"191\" height=\"189\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dreamt to become Pro in Math then having a good grip on Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences is mandatory. It is the ultimate guide for all high school students as it covers study resources for the concepts of chapter 6 Exponential Functions and Sequences. So, students can trust &#8230; <a title=\"Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers-chapter-6\/\" aria-label=\"More on Big Ideas Math Algebra 1 Answers Chapter 6 Exponential Functions and Sequences\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":89183,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-6-Exponential-Functions-and-Sequences.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/37573"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=37573"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/37573\/revisions"}],"predecessor-version":[{"id":90367,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/37573\/revisions\/90367"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89183"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=37573"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=37573"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=37573"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}