{"id":40223,"date":"2022-04-02T14:30:53","date_gmt":"2022-04-02T09:00:53","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=40223"},"modified":"2022-04-07T11:31:22","modified_gmt":"2022-04-07T06:01:22","slug":"big-ideas-math-algebra-2-answers-chapter-6","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-2-answers-chapter-6\/","title":{"rendered":"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions"},"content":{"rendered":"<p>Want to master in Algebra 2 Ch 6 Concepts like Exponential Growth and Decay Functions, Natural Base e, Logarithms, and its functions, properties of logarithms, etc.? Then, accessing this guide is the perfect solution for your concerns. <strong><a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-2-answers\/\">Big Ideas Math Algebra 2 Answers<\/a> Chapter 6 Exponential and Logarithmic Functions<\/strong> make you understand the topics quickly and clear all your subject queries. Moreover, the BIM Algebra 2 Ch 6 Solutions prevailing are written by the subject experts based on the guidelines of the latest common core curriculum. Hence, download the Big Ideas Math Algebra 2 Ch 6 Exponential and Logarithmic Functions &amp; enhance your maths skills.<\/p>\n<h2 class=\"entry-title\">Big Ideas Math Book Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions<\/h2>\n<p>BIM Algebra 2 Ch 6 Exponential and Logarithmic Functions covers Questions from Exercises 6.1 to 6.7, Review Tests, Chapter Tests, Cumulative Assessments, etc. With the help of this ultimate preparation guide provided performance task test, students can check their knowledge on Chapter 6 Exponential and Logarithmic Functions concepts. Tap on the link directly and practice each &amp; every lesson in <strong>Ch 6 Big Ideas Math Algebra 2 Solution Key Pdf<\/strong>. Access online Big Ideas Math Book Algebra 2 Ch 6 Exponential and Logarithmic Functions Answers pdf without paying a single penny.<\/p>\n<ul>\n<li><a href=\"#Exponential_and_Logarithmic_Functions_Maintaining_Mathematical_Proficiency\">Exponential and Logarithmic Functions Maintaining Mathematical Proficiency &#8211; Page 293<\/a><\/li>\n<li><a href=\"#Exponential_and_Logarithmic_Functions_Mathematical_Practices\">Exponential and Logarithmic Functions Mathematical Practices &#8211; Page 294<\/a><\/li>\n<li><a href=\"#Lesson_6.1_Exponential_Growth_and_Decay_Functions\">Lesson 6.1 Exponential Growth and Decay Functions &#8211; Page(295-302)<\/a><\/li>\n<li><a href=\"#Exponential_Growth_and_Decay_Functions_6.1_Exercises\">Exponential Growth and Decay Functions 6.1 Exercises &#8211; Page(300-302)<\/a><\/li>\n<li><a href=\"#Lesson_6.2_The_Natural_Base_e\">Lesson 6.2 The Natural Base e &#8211; Page(303-308)<\/a><\/li>\n<li><a href=\"#The_Natural_Base_e_6.2_Exercises\">The Natural Base e 6.2 Exercises &#8211; Page(307-308)<\/a><\/li>\n<li><a href=\"#Lesson_6.3_Logarithms_and_Logarithmic_Functions\">Lesson 6.3 Logarithms and Logarithmic Functions &#8211; Page(309-316)<\/a><\/li>\n<li><a href=\"#Logarithms_and_Logarithmic_Functions_6.3_Exercises\">Logarithms and Logarithmic Functions 6.3 Exercises &#8211; Page(314-316)<\/a><\/li>\n<li><a href=\"#Lesson_6.4_Transformations_of_Exponential_and_Logarithmic_Functions\">Lesson 6.4 Transformations of Exponential and Logarithmic Functions &#8211; Page(317-324)<\/a><\/li>\n<li><a href=\"#Transformations_of_Exponential_and_Logarithmic_Functions_6.4_Exercises\">Transformations of Exponential and Logarithmic Functions 6.4 Exercises &#8211; Page(322-324)<\/a><\/li>\n<li><a href=\"#Exponential_and_Logarithmic_Functions_Study_Skills:_Forming_a_Weekly_Study_Group\">Exponential and Logarithmic Functions Study Skills: Forming a Weekly Study Group &#8211; Page 325<\/a><\/li>\n<li><a href=\"#Exponential_and_Logarithmic_Functions_6.1\u20136.4_Quiz\">Exponential and Logarithmic Functions 6.1\u20136.4 Quiz &#8211; Page 326<\/a><\/li>\n<li><a href=\"#Lesson_6.5_Properties_of_Logarithms\">Lesson 6.5 Properties of Logarithms &#8211; Page(327-332)<\/a><\/li>\n<li><a href=\"#Properties_of_Logarithms_6.5_Exercises\">Properties of Logarithms 6.5 Exercises -Page(331-332)<\/a><\/li>\n<li><a href=\"#Lesson_6.6_Solving_Exponential_and_Logarithmic_Equations\">Lesson 6.6 Solving Exponential and Logarithmic Equations -Page(333-340)<\/a><\/li>\n<li><a href=\"#Solving_Exponential_and_Logarithmic_Equations_6.6_Exercises\">Solving Exponential and Logarithmic Equations 6.6 Exercises &#8211; Page(338-340)<\/a><\/li>\n<li><a href=\"#Lesson_6.7_Modeling_with_Exponential_and_Logarithmic_Functions\">Lesson 6.7 Modeling with Exponential and Logarithmic Functions &#8211; Page(341-348)<\/a><\/li>\n<li><a href=\"#Modeling_with_Exponential_and_Logarithmic_Functions_6.7_Exercises\">Modeling with Exponential and Logarithmic Functions 6.7 Exercises &#8211; Page(346-348)<\/a><\/li>\n<li><a href=\"#Exponential_and_Logarithmic_Functions_Performance_Task:_Measuring_Natural_Disasters\">Exponential and Logarithmic Functions Performance Task: Measuring Natural Disasters &#8211; Page 349<\/a><\/li>\n<li><a href=\"#Exponential_and_Logarithmic_Functions_Chapter_Review\">Exponential and Logarithmic Functions Chapter Review &#8211; Page(350-352)<\/a><\/li>\n<li><a href=\"#Exponential_and_Logarithmic_Functions_Chapter_Test\">Exponential and Logarithmic Functions Chapter Test &#8211; Page 353<\/a><\/li>\n<li><a href=\"#Exponential_and_Logarithmic_Functions_Cumulative_Assessment\">Exponential and Logarithmic Functions Cumulative Assessment &#8211; Page(354-355)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Exponential_and_Logarithmic_Functions_Maintaining_Mathematical_Proficiency\"><\/a>Exponential and Logarithmic Functions Maintaining Mathematical Proficiency<\/h3>\n<p><strong>Evaluate the expression.<\/strong><br \/>\nQuestion 1.<br \/>\n3 \u2022 2<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n(\u22122)<sup>5<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n\u2212(\\(\\frac{5}{6}\\))<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n(\\(\\frac{3}{4}\\))<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>Find the domain and range of the function represented by the graph.<\/strong><br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40228\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 1\" width=\"190\" height=\"131\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40229\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 2\" width=\"157\" height=\"134\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40230\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 3\" width=\"164\" height=\"128\" \/><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nConsider the expressions \u22124<sup>n<\/sup> and (\u22124)<sup>n<\/sup>, where n is an integer. For what values of n is each expression negative? positive? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Exponential_and_Logarithmic_Functions_Mathematical_Practices\"><\/a>Exponential and Logarithmic Functions Mathematical Practices<\/h3>\n<p>Mathematically proficient students know when it is appropriate to use general methods and shortcuts.<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Determine whether the data can be modeled by an exponential or linear function. Explain your reasoning. Then write the appropriate model and find y when x = 10<br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40231\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-4.1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 4.1\" width=\"244\" height=\"66\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40232\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-4.2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 4.2\" width=\"239\" height=\"64\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40233\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-4.3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 4.3\" width=\"235\" height=\"66\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40234\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-4.4.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 4.4\" width=\"237\" height=\"69\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_6.1_Exponential_Growth_and_Decay_Functions\"><\/a>Lesson 6.1 Exponential Growth and Decay Functions<\/h3>\n<p><strong>Essential Question<\/strong> What are some of the characteristics of the graph of an exponential function?You can use a graphing calculator to evaluate an exponential function. For example, consider the exponential function f(x) = 2<sup>x<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40235\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 1\" width=\"473\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-1.png 473w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-1-300x48.png 300w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Identifying Graphs of Exponential Functions<br \/>\nWork with a partner. Match each exponential function with its graph. Use a table of values to sketch the graph of the function, if necessary.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40236\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 2\" width=\"479\" height=\"451\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-2.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-2-300x282.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Characteristics of Graphs of Exponential Functions<br \/>\nWork with a partner. Use the graphs in Exploration 1 to determine the domain, range, and y-intercept of the graph of f(x) = b<sup>x<\/sup>, where b is a positive real number other than 1. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40237\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 3\" width=\"231\" height=\"184\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nWhat are some of the characteristics of the graph of an exponential function?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nIn Exploration 2, is it possible for the graph of f (x) =b x to have an x-intercept? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Tell whether the function represents exponential growth or exponential decay. Then graph the function.<\/strong><br \/>\nQuestion 1.<br \/>\ny = 4<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ny = (\\(\\frac{2}{3}\\))<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nf(x) = (0.25)<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nf(x) = (1.5)<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 2, the value of the car can be approximated by the model y = 25(0.9)<sup>t<\/sup>. Identify the annual percent decrease in the value of the car. Estimate when the value of the car will be $8000.<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 3, assume the world population increased by 1.5% each year. Write an equation to model this situation. Estimate the year when the world population was 7 billion.<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nThe amount y (in grams) of the radioactive isotope iodine-123 remaining after t hours is y = a(0.5)<sup>t\/13<\/sup>, where a is the initial amount (in grams). What percent of the iodine-123 decays each hour?<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 5, find the balance after 3 years when the interest is compounded daily.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Exponential_Growth_and_Decay_Functions_6.1_Exercises\"><\/a>Exponential Growth and Decay Functions 6.1 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nIn the exponential growth model y = 2.4(1.5)<sup>x<\/sup>, identify the initial amount, the growth factor, and the percent increase.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46314\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 1\" width=\"544\" height=\"42\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-1.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-1-300x23.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich characteristic of an exponential decay function does not belong with the other three? Explain your reasoning<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40238\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-4.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 4\" width=\"441\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-4.png 441w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-4-300x73.png 300w\" sizes=\"(max-width: 441px) 100vw, 441px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20138, evaluate the expression for (a) x = -2 and (b) x = 3.<\/strong><br \/>\nQuestion 3.<br \/>\n2<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46315\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 3\" width=\"138\" height=\"87\" \/><\/p>\n<p>Question 4.<br \/>\n4<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n8 \u2022 3<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46316\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-5.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 5\" width=\"262\" height=\"90\" \/><\/p>\n<p>Question 6.<br \/>\n6 \u2022 2<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n5 + 3<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46317\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-7.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 7\" width=\"273\" height=\"93\" \/><\/p>\n<p>Question 8.<br \/>\n2<sup>x<\/sup> \u2212 2<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 9\u201318, tell whether the function represents exponential growth or exponential decay. Then graph the function.<\/strong><br \/>\nQuestion 9.<br \/>\ny = 6<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46318\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-9.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 9\" width=\"592\" height=\"645\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-9.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-9-275x300.png 275w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 10.<br \/>\ny = 7<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\ny =(\\(\\frac{1}{6}\\))<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46319\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-11.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 11\" width=\"585\" height=\"698\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-11.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-11-251x300.png 251w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 12.<br \/>\ny =(\\(\\frac{1}{8}\\))<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\ny = (\\(\\frac{4}{3}\\))<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46320\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-13.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 13\" width=\"590\" height=\"693\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-13.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-13-255x300.png 255w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 14.<br \/>\ny = (\\(\\frac{2}{5}\\))<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\ny = (1.2)<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46321\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-15.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 15\" width=\"583\" height=\"640\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-15.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-15-273x300.png 273w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 16.<br \/>\ny = (0.75)<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\ny = (0.6)<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46322\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-17.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 17\" width=\"578\" height=\"658\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-17.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-17-264x300.png 264w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 18.<br \/>\ny = (1.8)<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>ANALYZING RELATIONSHIPS<\/strong> In Exercises 19 and 20, use the graph of f(x) = b<sup>x<\/sup> to identify the value of the base b.<br \/>\nQuestion 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40239\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-5.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 5\" width=\"147\" height=\"132\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46323\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-19.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 19\" width=\"544\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-19.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-19-300x32.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40240\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-6.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 6\" width=\"152\" height=\"137\" \/><br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe value of a mountain bike y (in dollars) can be approximated by the model y = 200(0.75)<sup>t<\/sup>, where t is the number of years since the bike was new.<br \/>\na. Tell whether the model represents exponential growth or exponential decay.<br \/>\nb. Identify the annual percent increase or decrease in the value of the bike.<br \/>\nc. Estimate when the value of the bike will be $50.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-21.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 21\" width=\"574\" height=\"206\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-21.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-21-300x108.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe population P(in thousands) of Austin, Texas, during a recent decade can be approximated by y = 494.29(1.03)<sup>t<\/sup>, where t is the number of years since the beginning of the decade.<br \/>\na. Tell whether the model represents exponential growth or exponential decay.<br \/>\nb. Identify the annual percent increase or decrease in population.<br \/>\nc. Estimate when the population was about 590,000.<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nIn 2006, there were approximately 233 million cell phone subscribers in the United States. During the next 4 years, the number of cell phone subscribers increased by about 6% each year.<br \/>\na. Write an exponential growth model giving the number of cell phone subscribers y (in millions) t years after 2006. Estimate the number of cell phone subscribers in 2008.<br \/>\nb. Estimate the year when the number of cell phone subscribers was about 278 million.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46325\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-23.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 23\" width=\"712\" height=\"311\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-23.png 712w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-23-300x131.png 300w\" sizes=\"(max-width: 712px) 100vw, 712px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou take a 325 milligram dosage of ibuprofen. During each subsequent hour, the amount of medication in your bloodstream decreases by about 29% each hour.<br \/>\na. Write an exponential decay model giving the amount y (in milligrams) of ibuprofen in your bloodstream t hours after the initial dose.<br \/>\nb. Estimate how long it takes for you to have 100\ue031milligrams of ibuprofen in your bloodstream.<br \/>\nAnswer:<\/p>\n<p><strong>JUSTIFYING STEPS<\/strong> In Exercises 25 and 26, justify each step in rewriting the exponential function.<br \/>\nQuestion 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40241\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-7.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 7\" width=\"322\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-7.png 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-7-300x97.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46326\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-25.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 25\" width=\"513\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-25.png 513w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-25-300x82.png 300w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40242\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-8.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 8\" width=\"330\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-8.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-8-300x102.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nWhen a plant or animal dies, it stops acquiring carbon-14 from the atmosphere. The amount y (in grams) of carbon-14 in the body of an organism after t years is y = a(0.5)<sup>t\/5730<\/sup>, where a is the initial amount (in grams). What percent of the carbon-14 is released each year?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46327\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-27.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 27\" width=\"455\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-27.png 455w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-27-300x115.png 300w\" sizes=\"(max-width: 455px) 100vw, 455px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe number y of duckweed fronds in a pond after t days is y = a(1230.25)<sup>t\/16<\/sup>, where a is the initial number of fronds. By what percent does the duckweed increase each day?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40243\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-9.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 9\" width=\"250\" height=\"151\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 29\u201336, rewrite the function in the form y = a(1 + r)<sup>t<\/sup> or y = a(1 &#8211; r)<sup>t<\/sup>. Then state the growth or decay rate.<\/strong><br \/>\nQuestion 29.<br \/>\ny = a(2)<sup>t\/3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46328\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-29.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 29\" width=\"376\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-29.png 376w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-29-300x139.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/p>\n<p>Question 30.<br \/>\ny = a(4)<sup>t\/6<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\ny = a(0.5)<sup>t\/12<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46329\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-31.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 31\" width=\"363\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-31.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-31-300x144.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 32.<br \/>\ny = a(0.25)<sup>t\/9<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\ny = a(\\(\\frac{2}{3}\\))<sup>t\/10<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46330\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-33.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 33\" width=\"338\" height=\"231\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-33.png 338w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-33-300x205.png 300w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><\/p>\n<p>Question 34.<br \/>\ny = a(\\(\\frac{5}{4}\\))<sup>t\/22<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\ny = a(2)<sup>8t<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46331\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-35.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 35\" width=\"337\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-35.png 337w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-35-300x154.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><\/p>\n<p>Question 36.<br \/>\ny = a(\\(\\frac{1}{3}\\))<sup>3t<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou deposit $5000 in an account that pays 2.25% annual interest. Find the balance after 5 years when the interest is compounded quarterly.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46332\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-37.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 37\" width=\"558\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-37.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-37-300x139.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nYou deposit $2200 into three separate bank accounts that each pay 3% annual interest. How much interest does each account earn after 6 years?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-10.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 10\" width=\"317\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-10.png 317w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-10-300x115.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nYou invest $500 in the stock of a company. The value of the stock decreases 2% each year. Describe and correct the error in writing a model for the value of the stock after t years.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40245\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-11.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 11\" width=\"327\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-11.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-11-300x103.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46333\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-39.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 39\" width=\"570\" height=\"127\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-39.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-39-300x67.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nYou deposit $250 in an account that pays 1.25% annual interest. Describe and correct the error in finding the balance after 3 years when the interest is compounded quarterly.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40246\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-12.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 12\" width=\"339\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-12.png 339w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-12-300x99.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 41\u2013 44, use the given information to find the amount A in the account earning compound interest after 6 years when the principal is $3500.<br \/>\nQuestion 41.<br \/>\nr = 2.16%, compounded quarterly<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46334\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-41.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 41\" width=\"272\" height=\"157\" \/><\/p>\n<p>Question 42.<br \/>\nr = 2.29%, compounded monthly<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\nr = 1.83%, compounded daily<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46335\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-43.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 43\" width=\"284\" height=\"159\" \/><\/p>\n<p>Question 44.<br \/>\nr = 1.26%, compounded monthly<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nA website recorded the number y of referrals it received from social media websites over a 10-year period. The results can be modeled by y = 2500(1.50)<sup>t<\/sup>, where t is the year and 0 \u2264 t\u2264 9. Interpret the values of a and b in this situation. What is the annual percent increase? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46336\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-45.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 45\" width=\"556\" height=\"137\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-45.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-45-300x74.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nConsider the graph of an exponential function of the form f (x) = ab<sup>x<\/sup>.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40247\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-13.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 13\" width=\"193\" height=\"151\" \/><br \/>\na. Determine whether the graph of f represents exponential growth or exponential decay.<br \/>\nb. What are the domain and range of the function? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says the graph of f(x) = 2<sup>x<\/sup> increases at a faster rate than the graph of g (x) = x<sup>2<\/sup> when x \u2265 0. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40248\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-14.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 14\" width=\"129\" height=\"119\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46337\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-47.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 47\" width=\"555\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-47.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-47-300x62.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nThe function f(x) = b<sup>x<\/sup> represents an exponential decay function. Write a second exponential decay function in terms of b and x.<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe population p of a small town after x years can be modeled by the function p = 6850(1.03)<sup>x<\/sup>. What is the average rate of change in the population over the first 6 years? Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46338\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-49.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 49\" width=\"548\" height=\"137\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-49.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-49-300x75.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>REASONING<\/strong><br \/>\nConsider the exponential function f(x) = ab<sup>x<\/sup>.<br \/>\na. Show that \\(\\frac{f(x+1)}{f(x)}\\) = b.<br \/>\nb. Use the equation in part (a) to explain why there is no exponential function of the form f(x) = ab<sup>x<\/sup> whose graph passes through the points in the table below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40249\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-15.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 15\" width=\"251\" height=\"61\" \/><br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe number E of eggs a Leghorn chicken produces per year can be modeled by the equation E = 179.2(0.89)<sup>w\/52<\/sup>, where w is the age (in weeks) of the chicken and w \u2265 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40250\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-16.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 16\" width=\"207\" height=\"144\" \/><br \/>\na. Identify the decay factor and the percent decrease.<br \/>\nb. Graph the model.<br \/>\nc. Estimate the egg production of a chicken that is 2.5 years old.d. Explain how you can rewrite the given equation so that time is measured in years rather than in weeks.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46339\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-51.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 51\" width=\"572\" height=\"606\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-51.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-51-283x300.png 283w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 52.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nYou buy a new stereo for $1300 and are able to sell it 4 years later for $275. Assume that the resale value of the stereo decays exponentially with time. Write an equation giving the resale value V(in dollars) of the stereo as a function of the time t (in years) since you bought it.<br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 53.<br \/>\nx<sup>9<\/sup> \u2022 x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46340\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-53.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 53\" width=\"214\" height=\"32\" \/><\/p>\n<p>Question 54.<br \/>\n\\(\\frac{x^{4}}{x^{3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n4x \u2022 6x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46341\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-55.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 55\" width=\"246\" height=\"30\" \/><\/p>\n<p>Question 56.<br \/>\n\\(\\left(\\frac{4 x^{8}}{2 x^{6}}\\right)<sup>4<\/sup>\\)<br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n\\(\\frac{x+3 x}{2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46342\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-57.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 57\" width=\"193\" height=\"54\" \/><\/p>\n<p>Question 58.<br \/>\n\\(\\frac{6x}{2}\\) + 4x<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n\\(\\frac{12x}{4x}\\) + 5x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46343\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.1-a-59.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.1 a 59\" width=\"201\" height=\"53\" \/><\/p>\n<p>Question 60.<br \/>\n(2x \u2022 3x<sup>5<\/sup>)<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_6.2_The_Natural_Base_e\"><\/a>Lesson 6.2 The Natural Base e<\/h3>\n<p><strong>Essential Question<\/strong> What is the natural base e?<br \/>\nSo far in your study of mathematics, you have worked with special numbers such as \u03c0 and i. Another special number is called the natural base and is denoted by e. The natural base e is irrational, so you cannot find its exact value.<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Approximating the Natural Base e<br \/>\nWork with a partner. One way to approximate the natural base e is to approximate the sum<br \/>\n1 + \\(\\frac{1}{1}+\\frac{1}{1 \\cdot 2}+\\frac{1}{1 \\cdot 2 \\cdot 3}+\\frac{1}{1 \\cdot 2 \\cdot 3 \\cdot 4}+\\cdots\\)<br \/>\nUse a spreadsheet or a graphing calculator to approximate this sum. Explain the steps you used. How many decimal places did you use in your approximation?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40251\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 1\" width=\"219\" height=\"184\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Approximating the Natural Base e<br \/>\nWork with a partner. Another way to approximate the natural base e is to consider the expression(1 + \\(\\frac{1}{x}\\))<sup>x<\/sup> .<br \/>\nAs x increases, the value of this expression approaches the value of e. Copy and complete the table. Then use the results in the table to approximate e. Compare this approximation to the one you obtained in Exploration 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40252\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 2\" width=\"460\" height=\"101\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-2.png 460w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-2-300x66.png 300w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><\/p>\n<p><strong>EXPLORATION 3<\/strong><\/p>\n<p>Graphing a Natural Base Function<br \/>\nWork with a partner. Use your approximate value of e in Exploration 1 or 2 to complete the table. Then sketch the graph of the natural base exponential function y =e<sup>x<\/sup>. You can use a graphing calculator and the e<sup>x<\/sup> key to check your graph. What are the domain and range of y = e<sup>x<\/sup>? Justify your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40253\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 3\" width=\"400\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-3.png 400w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-3-300x59.png 300w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 4.<br \/>\nWhat is the natural base e?<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nRepeat Exploration 3 for the natural base exponential function y = e<sup>-x<\/sup>. Then compare the graph of y = e<sup>x<\/sup> to the graph of y = e<sup>-x<\/sup>.<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nThe natural base e is used in a wide variety of real-life applications. Use the Internet or some other reference to research some of the real-life applications of e.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 1.<br \/>\ne<sup>7<\/sup> \u2022 e<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{24 e^{8}}{8 e^{5}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n(10e<sup>-3x<\/sup>)<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>Tell whether the function represents exponential growth or exponential decay. Then graph the function.<\/strong><br \/>\nQuestion 4.<br \/>\ny = \\(\\frac{1}{2}\\)e<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\ny = 4e<sup>-x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nf(x) = 2e<sup>2x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nYou deposit $4250 in an account that earns 5% annual interest compounded continuously. Compare the balance after 10 years with the accounts in Example 3.<br \/>\nAnswer:<\/p>\n<h3><a id=\"The_Natural_Base_e_6.2_Exercises\"><\/a>The Natural Base e 6.2 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat is the natural base e?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46344\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 1\" width=\"508\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-1.png 508w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-1-300x18.png 300w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nTell whether the function f(x) = \\(\\frac{1}{3}\\)e<sup>4x<\/sup> represents exponential growth or exponential decay. Explain.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u201312, simplify the expression.<\/strong><br \/>\nQuestion 3.<br \/>\ne<sup>3<\/sup> \u2022 e<sup>5<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46345\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 3\" width=\"161\" height=\"65\" \/><\/p>\n<p>Question 4.<br \/>\ne<sup>-4<\/sup> \u2022 e<sup>6<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{11 e^{9}}{22 e^{10}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46346\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 5\" width=\"169\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-5.png 169w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-5-150x150.png 150w\" sizes=\"(max-width: 169px) 100vw, 169px\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\frac{27 e^{7}}{3 e^{4}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n(5e<sup>7x<\/sup>)<sup>4<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46347\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 7\" width=\"176\" height=\"69\" \/><\/p>\n<p>Question 8.<br \/>\n(4e<sup>-2x<\/sup>)<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n\\(\\sqrt{9 e^{6 x}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46348\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 9\" width=\"182\" height=\"108\" \/><\/p>\n<p>Question 10.<br \/>\n\\(\\sqrt[3]{8 e^{12 x}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\ne<sup>x<\/sup> \u2022 e<sup>-6x<\/sup> \u2022 e<sup>8<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 11\" width=\"245\" height=\"61\" \/><\/p>\n<p>Question 12.<br \/>\ne<sup>x<\/sup> \u2022 e<sup>4<\/sup> \u2022 e<sup>x+3<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 13 and 14, describe and correct the error in simplifying the expression.<br \/>\nQuestion 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40254\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-4.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 4\" width=\"241\" height=\"79\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46350\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 13\" width=\"331\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-13.png 331w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-13-300x88.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40255\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 5\" width=\"234\" height=\"99\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 15\u201322, tell whether the function represents exponential growth or exponential decay. Then graph the function.<\/strong><br \/>\nQuestion 15.<br \/>\ny = e<sup>3x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 15\" width=\"570\" height=\"482\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-15.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-15-300x254.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 16.<br \/>\ny = e<sup>-2x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\ny = 2e<sup>-x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 17\" width=\"584\" height=\"489\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-17.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-17-300x251.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 18.<br \/>\ny = 3e<sup>2x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\ny = 0.5e<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 19\" width=\"568\" height=\"488\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-19.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-19-300x258.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 20.<br \/>\ny = 0.25e<sup>-3x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\ny = 0.4e<sup>-0.25x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 21\" width=\"541\" height=\"492\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-21.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-21-300x273.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 22.<br \/>\ny = 0.6e<sup>0.5x<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>ANALYZING EQUATIONS<\/strong> In Exercises 23\u201326, match the function with its graph. Explain your reasoning.<br \/>\nQuestion 23.<br \/>\ny = e<sup>2x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46355\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 23\" width=\"556\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-23.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-23-300x36.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 24.<br \/>\ny = e<sup>-2x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\ny = 4e<sup>-0.5x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 25\" width=\"548\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-25.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-25-300x31.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 26.<br \/>\ny = 0.75e<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40256\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-6.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 6\" width=\"365\" height=\"330\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-6.png 365w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-6-300x271.png 300w\" sizes=\"(max-width: 365px) 100vw, 365px\" \/><\/p>\n<p><strong>USING STRUCTURE<\/strong> In Exercises 27\u201330, use the properties of exponents to rewrite the function in the form y = a(1 + r)<sup>t<\/sup> or y = a(1 &#8211; r)<sup>t<\/sup>. Then find the percent rate of change.<br \/>\nQuestion 27.<br \/>\ny = e<sup>-0.25t<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46357\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 27\" width=\"370\" height=\"175\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-27.png 370w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-27-300x142.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><\/p>\n<p>Question 28.<br \/>\ny = e<sup>-0.75t<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\ny = 2e<sup>0.4t<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 29\" width=\"357\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-29.png 357w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-29-300x145.png 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><\/p>\n<p>Question 30.<br \/>\ny = 0.5e<sup>0.8t<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>USING TOOLS<\/strong> In Exercises 31\u201334, use a table of values or a graphing calculator to graph the function. Then identify the domain and range.<br \/>\nQuestion 31.<br \/>\ny = e<sup>x-2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 31\" width=\"568\" height=\"465\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-31.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-31-300x246.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 32.<br \/>\ny = e<sup>x+1<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\ny = 2e<sup>x<\/sup> + 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 33\" width=\"563\" height=\"460\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-33.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-33-300x245.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 34.<br \/>\ny = 3e<sup>x<\/sup> \u2212 5<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nInvestment accounts for a house and education earn annual interest compounded continuously. The balance H(in dollars) of the house fund after t years can be modeled by H = 3224e0.05t. The graph shows the balance in the education fund over time. Which account has the greater principal? Which account has a greater balance after 10 years?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40257\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 7\" width=\"232\" height=\"239\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46361\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 35\" width=\"596\" height=\"475\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-35.png 596w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-35-300x239.png 300w\" sizes=\"(max-width: 596px) 100vw, 596px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nTritium and sodium-22 decay over time. In a sample of tritium, the amount y (in milligrams) remaining after t years is given by y = 10e<sup>\u22120.0562t<\/sup>. The graph shows the amount of sodium-22 in a sample over time. Which sample started with a greater amount? Which has a greater amount after 10 years?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40258\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-8.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 8\" width=\"155\" height=\"162\" \/><br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nFind values of a, b, r, and q such that f(x) = ae<sup>rx<\/sup> and g(x) = be<sup>qx<\/sup> are exponential decay functions, but \\(\\frac{f(x)}{g(x)}\\) represents exponential growth.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 37\" width=\"558\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-37.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-37-300x62.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nExplain why A = P(1 + \\(\\frac{r}{n}\\))<sup>nt<\/sup> approximates A =Pe<sup>rt<\/sup> as n approaches positive infinity.<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>WRITING<\/strong><br \/>\nCan the natural base e be written as a ratio of two integers? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 39\" width=\"575\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-39.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-39-300x32.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend evaluates f(x) = e<sup>-x<\/sup> when x = 1000 and concludes that the graph of y = fx) has an x-intercept at (1000, 0). Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nYou invest $2500 in an account to save for college. Account 1 pays 6% annual interest compounded quarterly. Account 2 pays 4% annual interest compounded continuously. Which account should you choose to obtain the greater amount in 10 years? Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 41\" width=\"574\" height=\"339\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-41.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-41-300x177.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the graph to complete each statement.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40259\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 9\" width=\"133\" height=\"132\" \/><br \/>\na. f(x) approaches ____ as x approaches +\u221e.<br \/>\nb. f(x) approaches ____ as x approaches \u2212\u221e.<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe growth of Mycobacterium tuberculosis bacteria can be modeled by the function N(t) = ae<sup>0.166t<\/sup>, where N is the number of cells after t hours and a is the number of cells when t = 0.<br \/>\na. At 1:00 P.M., there are 30 M. tuberculosis bacteria in a sample. Write a function that gives the number of bacteria after 1:00 P.M.<br \/>\nb. Use a graphing calculator to graph the function in part (a).<br \/>\nc. Describe how to find the number of cells in the sample at 3:45 P.M.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 43\" width=\"555\" height=\"369\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-43.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-43-300x199.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Write the number in scientific notation.<\/strong><br \/>\nQuestion 44.<br \/>\n0.006<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n5000<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46366\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-45.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 45\" width=\"182\" height=\"32\" \/><\/p>\n<p>Question 46.<br \/>\n26,000,000<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n0.000000047<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46367\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-47.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 47\" width=\"289\" height=\"30\" \/><\/p>\n<p><strong>Find the inverse of the function. Then graph the function and its inverse.<\/strong><br \/>\nQuestion 48.<br \/>\ny = 3x + 5<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\ny = x<sup>2<\/sup> \u2212 1, x \u2264 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-49.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 49\" width=\"572\" height=\"526\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-49.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-49-300x276.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 50.<br \/>\ny = \\(\\sqrt{x+6}\\)<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\ny = x<sup>3<\/sup> \u2212 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46369\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-51.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.2 a 51\" width=\"389\" height=\"511\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-51.png 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.2-a-51-228x300.png 228w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><\/p>\n<h3><a id=\"Lesson_6.3_Logarithms_and_Logarithmic_Functions\"><\/a>Lesson 6.3 Logarithms and Logarithmic Functions<\/h3>\n<p><strong>Essential Question<\/strong> What are some of the characteristics of the graph of a logarithmic function?<br \/>\nEvery exponential function of the form f(x) = b<sup>x<\/sup>, where b is a positive real number other than 1, has an inverse function that you can denote by g(x) = log<sub>b<\/sub>x. This inverse function is called a logarithmic function with base b.<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Rewriting Exponential Equations<br \/>\nWork with a partner. Find the value of x in each exponential equation. Explain your reasoning. Then use the value of x to rewrite the exponential equation in its equivalent logarithmic form, x = log<sub>b<\/sub>y.<br \/>\na. 2<sup>x<\/sup> = 8<br \/>\nb. 3<sup>x<\/sup> = 9<br \/>\nc. 4<sup>x<\/sup> = 2<br \/>\nd. 5<sup>x<\/sup> = 1<br \/>\ne. 5<sup>x<\/sup> = \\(\\frac{1}{5}\\)<br \/>\nf. 8<sup>x<\/sup> = 4<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Graphing Exponential and Logarithmic Functions<br \/>\nWork with a partner. Complete each table for the given exponential function. Use the results to complete the table for the given logarithmic function. Explain your reasoning. Then sketch the graphs of f and g in the same coordinate plane.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40260\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 1\" width=\"429\" height=\"297\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-1.png 429w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-1-300x208.png 300w\" sizes=\"(max-width: 429px) 100vw, 429px\" \/><\/p>\n<p><strong>EXPLORATION 3<\/strong><\/p>\n<p>Characteristics of Graphs of LogarithmicFunctions<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40261\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-2.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 2\" width=\"228\" height=\"190\" \/><br \/>\nWork with a partner. Use the graphs you sketched in Exploration 2 to determine the domain, range, x-intercept, and asymptote of the graph of g(x) = log<sub>b<\/sub>x, where b is a positive real number other than 1. Explain your reasoning.<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 4.<br \/>\nWhat are some of the characteristics of the graph of a logarithmic function?<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nHow can you use the graph of an exponential function to obtain the graph of a logarithmic function?<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Rewrite the equation in exponential form.<\/strong><br \/>\nQuestion 1.<br \/>\nlog<sub>3<\/sub> 81 = 4<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nlog<sub>7<\/sub> 7 = 1<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nlog<sub>14<\/sub> 1 = 0<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nlog<sub>1\/2<\/sub> 32 = \u22125<br \/>\nAnswer:<\/p>\n<p><strong>Rewrite the equation in logarithmic form.<\/strong><br \/>\nQuestion 5.<br \/>\n7<sup>2<\/sup> = 49<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n50<sup>0<\/sup> = 1<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n4<sup>-1<\/sup> = \\(\\frac{1}{4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n256<sup>1\/8<\/sup> = 2<br \/>\nAnswer:<\/p>\n<p><strong>Evaluate the logarithm. If necessary, use a calculator and round your answer to three decimal places.<\/strong><br \/>\nQuestion 9.<br \/>\nlog<sub>2<\/sub> 32<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nlog<sub>27<\/sub> 3<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nlog 12<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nln 0.75<br \/>\nAnswer:<\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 13.<br \/>\n8<sup>log<sub>8 <\/sub>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nlog<sub>7<\/sub> 7<sup>\u22123x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nlog<sub>2<\/sub> 64<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\ne<sup>ln 20<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nFind the inverse of y = 4<sup>x<\/sup>.<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\nFind the inverse of y = ln(x\u2212 5).<br \/>\nAnswer:<\/p>\n<p><strong>Graph the function.<\/strong><br \/>\nQuestion 19.<br \/>\ny = log<sub>2<\/sub> x<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\nf(x) = log<sub>5<\/sub> x<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\ny = log<sub>1\/2<\/sub> x<br \/>\nAnswer:<\/p>\n<h3><a id=\"Logarithms_and_Logarithmic_Functions_6.3_Exercises\"><\/a>Logarithms and Logarithmic Functions 6.3 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nA logarithm with base 10 is called a(n) ___________ logarithm.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 1\" width=\"531\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-1.png 531w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-1-300x18.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe expression log<sub>3<\/sub> 9 is read as ______________.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe the relationship between y = 7<sup>x<\/sup> and y = log<sub>7<\/sub> x.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46371\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-3.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 3\" width=\"519\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-3.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-3-300x19.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40262\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-3.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 3\" width=\"431\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-3.png 431w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-3-300x58.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 5\u201310, rewrite the equation in exponential form.<\/strong><br \/>\nQuestion 5.<br \/>\nlog<sub>3<\/sub> 9 = 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46372\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-5.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 5\" width=\"235\" height=\"32\" \/><\/p>\n<p>Question 6.<br \/>\nlog<sub>4<\/sub> 4 = 1<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nlog<sub>6<\/sub> 1 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46373\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-7.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 7\" width=\"218\" height=\"31\" \/><\/p>\n<p>Question 8.<br \/>\nlog<sub>7 <\/sub>343 = 3<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nlog<sub>1\/2<\/sub> 16 =\u22124<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46374\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-9.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 9\" width=\"306\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-9.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-9-300x57.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><\/p>\n<p>Question 10.<br \/>\nlog<sub>3<\/sub> \\(\\frac{1}{3}\\) = \u22121<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 11\u201316, rewrite the equation in logarithmic form.<\/strong><br \/>\nQuestion 11.<br \/>\n6<sup>2<\/sup> = 36<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46375\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-11.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 11\" width=\"242\" height=\"33\" \/><\/p>\n<p>Question 12.<br \/>\n12<sup>0<\/sup> = 1<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n16<sup>-1<\/sup> = \\(\\frac{1}{16}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46376\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-13.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 13\" width=\"290\" height=\"55\" \/><\/p>\n<p>Question 14.<br \/>\n5<sup>-2<\/sup> = \\(\\frac{1}{25}\\)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n125<sup>2\/3<\/sup> = 25<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46377\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-15.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 15\" width=\"299\" height=\"55\" \/><\/p>\n<p>Question 16.<br \/>\n49<sup>1\/2<\/sup> = 7<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 17\u201324, evaluate the logarithm.<\/strong><br \/>\nQuestion 17.<br \/>\nlog<sub>3<\/sub> 81<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46378\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-17.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 17\" width=\"235\" height=\"34\" \/><\/p>\n<p>Question 18.<br \/>\nlog<sub>7<\/sub> 49<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nlog<sub>3<\/sub> 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46379\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-19.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 19\" width=\"128\" height=\"35\" \/><\/p>\n<p>Question 20.<br \/>\nlog<sub>1\/2<\/sub> 1<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\nlog<sub>5<\/sub> \\(\\frac{1}{625}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46380\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-21.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 21\" width=\"254\" height=\"53\" \/><\/p>\n<p>Question 22.<br \/>\nlog<sub>8<\/sub> \\(\\frac{1}{512}\\)<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nlog<sub>4<\/sub> 0.25<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46381\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-23.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 23\" width=\"350\" height=\"49\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-23.png 350w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-23-300x42.png 300w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/p>\n<p>Question 24.<br \/>\nlog<sub>10<\/sub> 0.001<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nOrder the logarithms from least value to greatest value.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40263\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-4.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 4\" width=\"317\" height=\"48\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-4.png 317w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-4-300x45.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46382\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-25.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 25\" width=\"533\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-25.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-25-300x35.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why the expressions log<sub>2<\/sub>(\u22121) and log<sub>1<\/sub> 1 are not defined.<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 27\u201332, evaluate the logarithm using a calculator. Round your answer to three decimal places.<\/strong><br \/>\nQuestion 27.<br \/>\nlog 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-27.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 27\" width=\"164\" height=\"31\" \/><\/p>\n<p>Question 28.<br \/>\nln 12<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nln \\(\\frac{1}{3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46384\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-29.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 29\" width=\"161\" height=\"54\" \/><\/p>\n<p>Question 30.<br \/>\nlog \\(\\frac{2}{7}\\)<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n3 ln 0.5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46385\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-31.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 31\" width=\"201\" height=\"27\" \/><\/p>\n<p>Question 32.<br \/>\nlog 0.6 + 1<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nSkydivers use an instrument called an altimeter to track their altitude as they fall. The altimeter determines altitude by measuring air pressure. The altitude h (in meters) above sea level is related to the air pressure P(in pascals) by the function shown in the diagram. What is the altitude above sea level when the air pressure is 57,000 pascals?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40264\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-5.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 5\" width=\"362\" height=\"178\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-5.png 362w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-5-300x148.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46386\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-33.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 33\" width=\"560\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-33.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-33-300x83.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe pH value for a substance measures how acidic or alkaline the substance is. It is given by the formula pH = \u2212log[H<sup>+<\/sup>], where H<sup>+<\/sup> is the hydrogen ion concentration (in moles per liter). Find the pH of each substance.<br \/>\na. baking soda: [H<sup>+<\/sup>] = 10<sup>-8<\/sup> moles per liter<br \/>\nb. vinegar: [H<sup>+<\/sup>] = 10<sup>-3<\/sup> moles per liter<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 35\u201340, simplify the expression.<\/strong><br \/>\nQuestion 35.<br \/>\n7<sup>log<sub>7<\/sub>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46387\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-35.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 35\" width=\"124\" height=\"34\" \/><\/p>\n<p>Question 36.<br \/>\n3<sup>log<sub>3 <\/sub>5x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\ne<sup>ln4<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46388\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-37.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 37\" width=\"109\" height=\"31\" \/><\/p>\n<p>Question 38.<br \/>\n10<sup>log 15<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\nlog<sub>3<\/sub> 3<sup>2x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46389\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-39.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 39\" width=\"147\" height=\"37\" \/><\/p>\n<p>Question 40.<br \/>\nln e<sup>x + 1<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in rewriting 4<sup>\u22123<\/sup> = \\(\\frac{1}{64}\\) in logarithmic form.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40265\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-6.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 6\" width=\"207\" height=\"69\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46390\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-41.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 41\" width=\"404\" height=\"94\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-41.png 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-41-300x70.png 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in simplifying the expression log<sub>4<\/sub> 64<sup>x<\/sup>.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40266\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-7.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 7\" width=\"272\" height=\"116\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 43\u201352, find the inverse of the function.<\/strong><br \/>\nQuestion 43.<br \/>\ny = 0.3<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46391\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-43.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 43\" width=\"363\" height=\"136\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-43.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-43-300x112.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 44.<br \/>\ny = 11<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\ny = log<sub>2<\/sub> x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-45.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 45\" width=\"336\" height=\"137\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-45.png 336w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-45-300x122.png 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><\/p>\n<p>Question 46.<br \/>\ny = log<sub>1\/5<\/sub> x<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\ny = ln(x \u2212 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46393\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-47.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 47\" width=\"402\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-47.png 402w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-47-300x128.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p>\n<p>Question 48.<br \/>\ny = ln 2x<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\ny = e<sup>3x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46394\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-49.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 49\" width=\"363\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-49.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-49-300x145.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 50.<br \/>\ny = e<sup>x-4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\ny = 5<sup>x<\/sup> \u2212 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-51.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 51\" width=\"423\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-51.png 423w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-51-300x123.png 300w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><\/p>\n<p>Question 52.<br \/>\ny = 13 + log x<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe wind speed s (in miles per hour) near the center of a tornado can be modeled by s = 93 log d + 65, where d is the distance (in miles) that the tornado travels.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40267\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-8.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 8\" width=\"177\" height=\"196\" \/><br \/>\na. In 1925, a tornado traveled 220 miles through three states. Estimate the wind speed near the center of the tornado.<br \/>\nb. Find the inverse of the given function. Describe what the inverse represents.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46396\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-53.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 53\" width=\"575\" height=\"438\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-53.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-53-300x229.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 54.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe energy magnitude M of an earthquake can be modeled by M = \\(\\frac{2}{3}\\)log E \u2212 9.9, where E is the amount of energy released (in ergs).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40268\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-9.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 9\" width=\"317\" height=\"148\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-9.png 317w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-9-300x140.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><br \/>\na. In 2011, a powerful earthquake in Japan, caused by the slippage of two tectonic plates along a fault, released 2.24 \u00d7 10<sup>28<\/sup> ergs. What was the energy magnitude of the earthquake?<br \/>\nb. Find the inverse of the given function. Describe what the inverse represents.<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 55\u201360, graph the function.<\/strong><br \/>\nQuestion 55.<br \/>\ny = log<sub>4<\/sub> x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46397\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-55.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 55\" width=\"573\" height=\"647\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-55.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-55-266x300.png 266w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 56.<br \/>\ny = log<sub>6<\/sub> x<br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\ny = log<sub>1\/3<\/sub> x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-57.1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 57.1\" width=\"562\" height=\"584\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-57.1.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-57.1-289x300.png 289w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46399\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-57.2.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 57.2\" width=\"373\" height=\"307\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-57.2.png 373w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-57.2-300x247.png 300w\" sizes=\"(max-width: 373px) 100vw, 373px\" \/><\/p>\n<p>Question 58.<br \/>\ny = log<sub>1\/4<\/sub> x<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\ny = log<sub>2<\/sub> x \u2212 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46400\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-59.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 59\" width=\"580\" height=\"729\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-59.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-59-239x300.png 239w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 60.<br \/>\ny = log<sub>3<\/sub>(x + 2)<br \/>\nAnswer:<\/p>\n<p><strong>USING TOOLS<\/strong> In Exercises 61\u201364, use a graphing calculator to graph the function. Determine the domain, range, and asymptote of the function.<br \/>\nQuestion 61.<br \/>\ny = log(x+ 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46401\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-61.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 61\" width=\"560\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-61.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-61-300x118.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 62.<br \/>\ny = \u2212ln x<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\ny = ln(\u2212x)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46402\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-63.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 63\" width=\"519\" height=\"234\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-63.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-63-300x135.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 64.<br \/>\ny = 3 \u2212 log x<br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend states that every logarithmic function will pass through the point (1, 0). Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46403\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-65.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 65\" width=\"590\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-65.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-65-300x45.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 66.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nRank the functions in order from the least average rate of change to the greatest average rate of change over the interval 1 \u2264 x \u2264 10.<br \/>\na. y = log<sub>6<\/sub> x<br \/>\nb. y = log<sub>3\/5<\/sub> x<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40269\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-10.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 10\" width=\"299\" height=\"133\" \/><br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nBiologists have found that the length \u2113 (in inches) of an alligator and its weight w (in pounds) are related by the function \u2113 = 27.1 ln w \u2212 32.8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40270\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-11.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 11\" width=\"245\" height=\"121\" \/><br \/>\na. Use a graphing calculator to graph the function.<br \/>\nb. Use your graph to estimate the weight of an alligator that is 10 feet long.<br \/>\nc. Use the zero feature to find the x-intercept of the graph of the function. Does this x-value make sense in the context of the situation? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46404\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-67.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 67\" width=\"579\" height=\"327\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-67.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-67-300x169.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 68.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe figure shows the graphs of the two functions f and g.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40271\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-12.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 12\" width=\"203\" height=\"129\" \/><br \/>\na. Compare the end behavior of the logarithmic function g to that of the exponential function f.<br \/>\nb. Determine whether the functions are inverse functions. Explain.<br \/>\nc. What is the base of each function? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 69.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA study in Florida found that the number s of fish species in a pool or lake can be modeled by the function s = 30.6 \u2212 20.5 log A + 3.8(log A)<sup>2<\/sup><br \/>\nwhere A is the area (in square meters) of the pool or lake.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-13.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 13\" width=\"230\" height=\"108\" \/><br \/>\na. Use a graphing calculator to graph the function on the domain 200 \u2264 A \u2264 35,000.<br \/>\nb. Use your graph to estimate the number of species in a lake with an area of 30,000 square meters.<br \/>\nc. Use your graph to estimate the area of a lake that contains six species of fish.<br \/>\nd. Describe what happens to the number of fish species as the area of a pool or lake increases. Explain why your answer makes sense.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46405\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-69.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 69\" width=\"583\" height=\"395\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-69.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-69-300x203.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 70.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nWrite a logarithmic function that has an output of \u22124. Then sketch the graph of your function.<br \/>\nAnswer:<\/p>\n<p>Question 71.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nEvaluate each logarithm. (Hint: For each logarithm log<sub>b<\/sub> x, rewrite b and x as powers of the same base.)<br \/>\na. log<sub>125<\/sub> 25<br \/>\nb. log<sub>8<\/sub> 32<br \/>\nc. log<sub>27<\/sub> 81<br \/>\nd. log<sub>4<\/sub> 128<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-71.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 71\" width=\"257\" height=\"208\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p>Let f(x) = \\(\\sqrt [ 3 ]{ x }\\). Write a rule for g that represents the indicated transformation of the graph of f.<br \/>\nQuestion 72.<br \/>\ng(x) = \u2212f(x)<br \/>\nAnswer:<\/p>\n<p>Question 73.<br \/>\ng(x) = f (\\(\\frac{1}{2}\\)x )<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46407\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-73.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 73\" width=\"227\" height=\"61\" \/><\/p>\n<p>Question 74.<br \/>\ng(x) = f(\u2212x) + 3<br \/>\nAnswer:<\/p>\n<p>Question 75.<br \/>\ng(x) = f(x+ 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46408\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-75.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 75\" width=\"263\" height=\"41\" \/><\/p>\n<p><strong>Identify the function family to which f belongs. Compare the graph of f to the graph of its parent.<\/strong><br \/>\nQuestion 76.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40273\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-14.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 14\" width=\"151\" height=\"107\" \/><br \/>\nAnswer:<\/p>\n<p>Question 77.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40274\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-15.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 15\" width=\"145\" height=\"105\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46409\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-77.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 a 77\" width=\"571\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-77.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-a-77-300x30.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 78.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40275\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-6.3-16.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions 6.3 16\" width=\"145\" height=\"108\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_6.4_Transformations_of_Exponential_and_Logarithmic_Functions\"><\/a>Lesson 6.4 Transformations of Exponential and Logarithmic Functions<\/h3>\n<p><strong>Essential Question<\/strong> How can you transform the graphs of exponential and logarithmic functions?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Identifying Transformations<br \/>\nWork with a partner. Each graph shown is a transformation of the parent function<br \/>\nf(x) = e<sup>x<\/sup> or f(x) = ln x.<br \/>\nMatch each function with its graph. Explain your reasoning. Then describe the transformation of f represented by g.<br \/>\na. g(x) = e<sup>x+2<\/sup> \u2212 3<br \/>\nb. g(x) = \u2212e<sup>x+2<\/sup> + 1<br \/>\nc. g(x) = e<sup>x-2<\/sup> \u2212 1<br \/>\nd. g(x) = ln(x + 2)<br \/>\ne. g(x) = 2 + ln x<br \/>\nf. g(x) = 2 + ln(\u2212x)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40276\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-1.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 1\" width=\"445\" height=\"472\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-1.png 445w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-1-283x300.png 283w\" sizes=\"(max-width: 445px) 100vw, 445px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Characteristics of Graphs<br \/>\nWork with a partner. Determine the domain, range, and asymptote of each function in Exploration 1. Justify your answers.<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you transform the graphs of exponential and logarithmic functions?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nFind the inverse of each function in Exploration 1. Then check your answer by using a graphing calculator to graph each function and its inverse in the same viewing window.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40277\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-2.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 2\" width=\"229\" height=\"168\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Describe the transformation of f represented by g. Then graph each function.<\/strong><br \/>\nQuestion 1.<br \/>\nf(x) = 2<sup>x<\/sup>, g(x) = 2<sup>x-3<\/sup> + 1<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nf(x) = e<sup>-x<\/sup>, g(x) = e<sup>-x<\/sup> \u2212 5<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nf(x) = 0.4<sup>x<\/sup>, g(x) = 0.4<sup>-2x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nf(x) = e<sup>x<\/sup>, g(x) = \u2212e<sup>x+6<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>Describe the transformation of f represented by g. Then graph each function.<\/strong><br \/>\nQuestion 5.<br \/>\nf(x) = log<sub>2<\/sub>x, g(x) = \u22123 log<sub>2<\/sub>x<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nf(x) = log<sub>1\/4<\/sub>x, g(x) = log<sub>1\/4<\/sub>(4x) \u2212 5<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nLet the graph of g be a horizontal stretch by a factor of 3, followed by a translation 2 units up of the graph of f(x) = e<sup>-x<\/sup>. Write a rule for g.<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nLet the graph of g be a reflection in the y-axis, followed by a translation 4 units to the left of the graph of f(x) = log x. Write a rule for g.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Transformations_of_Exponential_and_Logarithmic_Functions_6.4_Exercises\"><\/a>Transformations of Exponential and Logarithmic Functions 6.4 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nGiven the function f(x) = ab<sup>x-h<\/sup> + k, describe the effects of a, h, and k on the graph of the function.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46410\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-1.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 1\" width=\"561\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-1.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-1-300x74.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe graph of g(x) = log4(\u2212x) is a reflection in the __________ of the graph of f(x) = log<sub>4<\/sub>x,<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20136, match the function with its graph. Explain your reasoning.<\/strong><br \/>\nQuestion 3.<br \/>\nf(x) = 2<sup>x+2<\/sup> \u2212 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46411\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-3.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 3\" width=\"567\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-3.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-3-300x27.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 4.<br \/>\ng(x) = 2<sup>x+2<\/sup> + 2<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nh(x) = 2<sup>x-2<\/sup> \u2212 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46412\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-5.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 5\" width=\"571\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-5.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-5-300x31.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 6.<br \/>\nk(x) = 2<sup>x-2<\/sup> + 2<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40278\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-3.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 3\" width=\"356\" height=\"303\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-3.png 356w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-3-300x255.png 300w\" sizes=\"(max-width: 356px) 100vw, 356px\" \/><\/p>\n<p><strong>In Exercises 7\u201316, describe the transformation of f represented by g. Then graph each function.<\/strong><br \/>\nQuestion 7.<br \/>\nf(x) = 3<sup>x<\/sup>, g(x) = 3<sup>x<\/sup> + 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46413\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-7.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 7\" width=\"580\" height=\"377\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-7.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-7-300x195.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 8.<br \/>\nf(x) = 4<sup>x<\/sup>, g(x) = 4<sup>x<\/sup> \u2212 8<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nf(x) = e<sup>x<\/sup>, g(x) = e<sup>x<\/sup> \u2212 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46414\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-9.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 9\" width=\"605\" height=\"448\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-9.png 605w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-9-300x222.png 300w\" sizes=\"(max-width: 605px) 100vw, 605px\" \/><\/p>\n<p>Question 10.<br \/>\nf(x) = e<sup>x<\/sup>, g(x) = e<sup>x<\/sup> + 4<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nf(x) = 2<sup>x<\/sup>, g(x) = 2<sup>x-7<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46415\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-11.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 11\" width=\"578\" height=\"400\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-11.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-11-300x208.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 12.<br \/>\nf(x) = 5<sup>x<\/sup>, g(x) = 5<sup>x+1<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nf(x) = e<sup>-x<\/sup>, g(x) = e<sup>-x<\/sup> + 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46416\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-13.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 13\" width=\"570\" height=\"421\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-13.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-13-300x222.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 14.<br \/>\nf(x) = e<sup>-x<\/sup>, g(x) = e<sup>-x<\/sup> \u2212 9<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nf(x) = (\\(\\frac{1}{4}\\))<sup>x<\/sup>, g (x) = (\\(\\frac{1}{4}\\))<sup>x-3<\/sup> + 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46417\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-15.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 15\" width=\"532\" height=\"438\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-15.png 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-15-300x247.png 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>Question 16.<br \/>\nf(x) = (\\(\\frac{1}{3}\\))<sup>x<\/sup>, g(x) = (\\(\\frac{1}{3}\\))<sup>x+2<\/sup> \u2212 \\(\\frac{2}{3}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 17\u201324, describe the transformation of f represented by g. Then graph each function.<\/strong><br \/>\nQuestion 17.<br \/>\nf(x) = e<sup>x<\/sup>, g(x) = e<sup>2x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46418\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-17.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 17\" width=\"577\" height=\"334\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-17.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-17-300x174.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 18.<br \/>\nf(x) = e<sup>x<\/sup>, g (x) =4\u20143 e<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nf(x) = 2<sup>x<\/sup>, g(x) = \u22122<sup>x-3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46419\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-19.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 19\" width=\"539\" height=\"419\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-19.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-19-300x233.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 20.<br \/>\nf(x) = 4<sup>x<\/sup>, g(x) = 4<sup>0.5x-5<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\nf(x) = e<sup>-x<\/sup>, g(x) = 3e<sup>-6x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46420\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-21.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 21\" width=\"572\" height=\"333\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-21.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-21-300x175.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 22.<br \/>\nf(x) = e<sup>-x<\/sup>, g(x) = e<sup>-5x<\/sup> + 2<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nf(x) = (\\(\\frac{1}{2}\\))<sup>x<\/sup>, g(x) = 6 (\\(\\frac{1}{2}\\))<sup>x+5<\/sup> \u2212 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46421\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-23.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 23\" width=\"549\" height=\"428\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-23.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-23-300x234.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 24.<br \/>\nf(x) = (\\(\\frac{3}{4}\\))<sup>x<\/sup>, g(x) = \u2212(\\(\\frac{3}{4}\\)) <sup>-7<\/sup> + 1<br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 25 and 26, describe and correct the error in graphing the function.<br \/>\nQuestion 25.<br \/>\nf(x) = 2<sup>x<\/sup> + 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40279\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-4.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 4\" width=\"327\" height=\"138\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-4.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-4-300x127.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-25.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 25\" width=\"561\" height=\"349\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-25.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-25-300x187.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 26.<br \/>\nf(x) = 3<sup>-x<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40280\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-5.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 5\" width=\"318\" height=\"131\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-5.png 318w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-5-300x124.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 27\u201330, describe the transformation of f represented by g. Then graph each function.<\/strong><br \/>\nQuestion 27.<br \/>\nf(x) = log<sub>4<\/sub> x, g(x) = 3 log<sub>4<\/sub> x \u2212 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46423\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-27.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 27\" width=\"567\" height=\"421\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-27.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-27-300x223.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 28.<br \/>\nf(x) = log<sub>1\/3<\/sub> x, g(x) = log<sub>1\/3<\/sub>(\u2212x) + 6<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nf(x) = log<sub>1\/5<\/sub> x, g(x) = \u2212 log<sub>1\/5<\/sub>(x \u2212 7)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46424\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-29.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 29\" width=\"541\" height=\"351\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-29.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-29-300x195.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 30.<br \/>\nf(x) = log<sub>2<\/sub> x, g(x) = log<sub>2<\/sub>(x + 2) \u2212 3<br \/>\nAnswer:<\/p>\n<p><strong>ANALYZING RELATIONSHIPS<\/strong> In Exercises 31\u201334, match the function with the correct transformation of the graph of f. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40281\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-6.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 6\" width=\"174\" height=\"152\" \/><br \/>\nQuestion 31.<br \/>\ny = f(x\u2212 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46425\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-31.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 31\" width=\"511\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-31.png 511w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-31-300x36.png 300w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><\/p>\n<p>Question 32.<br \/>\ny = f(x + 2)<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\ny = 2f(x)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46426\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-33.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 33\" width=\"532\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-33.png 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-33-300x33.png 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>Question 34.<br \/>\ny = f(2x)<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40282\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-7.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 7\" width=\"355\" height=\"310\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-7.png 355w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-7-300x262.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><\/p>\n<p><strong>In Exercises 35\u201338, write a rule for g that represents the indicated transformations of the graph of f.<\/strong><br \/>\nQuestion 35.<br \/>\nf(x) = 5<sup>x<\/sup>; translation 2 units down, followed by a reflection in the y-axis<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46427\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-35.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 35\" width=\"586\" height=\"294\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-35.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-35-300x151.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 36.<br \/>\nf(x) = (\\(\\frac{2}{3}\\))<sup>x<\/sup>; reflection in the x-axis, followed by a vertical stretch by a factor of 6 and a translation 4 units left<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\nf(x) = e<sup>x<\/sup>; horizontal shrink by a factor of \\(\\frac{1}{2}\\), followed by a translation 5 units up<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46428\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-37.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 37\" width=\"565\" height=\"296\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-37.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-37-300x157.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 38.<br \/>\nf(x) =e<sup>-x<\/sup>; translation 4 units right and 1 unit down, followed by a vertical shrink by a factor of \\(\\frac{1}{3}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 39\u201342, write a rule for g that represents the indicated transformation of the graph of f.<\/strong><br \/>\nQuestion 39.<br \/>\nf(x) = log<sub>6<\/sub> x; vertical stretch by a factor of 6, followed by a translation 5 units down<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46429\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-39.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 39\" width=\"576\" height=\"302\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-39.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-39-300x157.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 40.<br \/>\nf(x) = log<sub>2<\/sub> x; reflection in the x-axis, followed by a translation 9 units left<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\nf(x) = log<sub>1\/2<\/sub> x; translation 3 units left and 2 units up, followed by a reflection in the y-axis<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46430\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-41.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 41\" width=\"543\" height=\"302\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-41.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-41-300x167.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 42.<br \/>\nf(x) = ln x; translation 3 units right and 1 unit up, followed by a horizontal stretch by a factor of 8<br \/>\nAnswer:<\/p>\n<p><strong>JUSTIFYING STEPS<\/strong> In Exercises 43 and 44, justify each step in writing a rule for g that represents the indicated transformations of the graph of f.<br \/>\nQuestion 43.<br \/>\nf(x) = log<sub>7<\/sub> x; reflection in the x-axis, followed by a translation 6 units down<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40283\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-8.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 8\" width=\"321\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-8.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-8-300x102.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46431\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-43.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 43\" width=\"468\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-43.png 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-43-300x90.png 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 44.<br \/>\nf(x) = 8x; vertical stretch by a factor of 4, followed by a translation 1 unit up and 3 units left<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40284\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-9.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 9\" width=\"328\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-9.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-9-300x105.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>USING STRUCTURE<\/strong> In Exercises 45\u201348, describe the transformation of the graph of f represented by the graph of g. Then give an equation of the asymptote.<br \/>\nQuestion 45.<br \/>\nf(x) = e<sup>x<\/sup>, g(x) = e<sup>x<\/sup> + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46432\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-45.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 45\" width=\"591\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-45.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-45-300x30.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p>Question 46.<br \/>\nf(x) = 3<sup>x<\/sup>, g(x) = 3<sup>x-9<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\nf(x) = ln x, g(x) = ln(x + 6)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46433\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-47.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 47\" width=\"563\" height=\"52\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-47.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-47-300x28.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 48.<br \/>\nf(x) = log<sub>1\/5<\/sub> x, g(x) = log<sub>1\/5<\/sub> x + 13<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe slope Sof a beach is related to the average diameter d(in millimeters) of the sand particles on the beach by the equation S = 0.159 + 0.118 log d. Describe the transformation of f(d ) = log d represented by S. Then use the function to determine the slope of a beach for each sand type below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40285\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-10.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 10\" width=\"281\" height=\"163\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46434\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-49.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 49\" width=\"573\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-49.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-49-300x136.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graphs of f(x) = b<sup>x<\/sup> and g(x) = (\\(\\frac{1}{b}\\))<sup>x<\/sup> are shown for b = 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40286\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-11.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 11\" width=\"167\" height=\"156\" \/><br \/>\na. Use the graph to describe a transformation of the graph of f that results in the graph of g.<br \/>\nb. Does your answer in part (a) change when 0 &lt; b &lt; 1? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims a single transformation of f(x) = log x can result in a function g whose graph never intersects the graph of f. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46435\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-51.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 51\" width=\"486\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-51.png 486w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-51-300x36.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p>Question 52.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nIs it possible to transform the graph of f(x) = e<sup>x<\/sup> to obtain the graph of g(x) = ln x? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nDetermine whether each statement is always, sometimes, or never true. Explain your reasoning.<br \/>\na. A vertical translation of the graph of f(x) = log x changes the equation of the asymptote.<br \/>\nb. A vertical translation of the graph of f(x) = e<sup>x<\/sup> changes the equation of the asymptote.<br \/>\nc. A horizontal shrink of the graph of f(x) = log x does not change the domain.<br \/>\nd. The graph of g(x) = ab<sup>x-h<\/sup> + k does not intersect the x-axis.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46436\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-53.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 53\" width=\"568\" height=\"247\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-53.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-53-300x130.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 54.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe amount P (in grams) of 100 grams of plutonium-239 that remains after t years can be modeled by P= 100(0.99997)<sup>t<\/sup>.<br \/>\na. Describe the domain and range of the function.<br \/>\nb. How much plutonium-239 is present after 12,000 years?<br \/>\nc. Describe the transformation of the function if the initial amount of plutonium were 550 grams.<br \/>\nd. Does the transformation in part (c) affect the domain and range of the function? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nConsider the graph of the function h(x) = e<sup>-x-2<\/sup>. Describe the transformation of the graph of f(x) = e<sup>-x<\/sup> represented by the graph of h. Then describe the transformation of the graph of g(x) = e<sup>x<\/sup> represented by the graph of h. Justify your answers.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46437\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-55.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 55\" width=\"595\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-55.png 595w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-55-300x44.png 300w\" sizes=\"(max-width: 595px) 100vw, 595px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite a function of the form y = ab<sup>x-h<\/sup> + k whose graph has a y-intercept of 5 and an asymptote of y = 2.<br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Perform the indicated operation.<\/strong><br \/>\nQuestion 57.<br \/>\nLet f(x) = x<sup>4<\/sup> and g(x) = x<sup>2<\/sup>. Find ( fg)(x). Then evaluate the product when x = 3.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46438\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-57.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 57\" width=\"380\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-57.png 380w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-57-300x135.png 300w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><\/p>\n<p>Question 58.<br \/>\nLet f(x) = 4x<sup>6<\/sup> and g(x) = 2x<sup>3<\/sup>. Find (\\(\\frac{f}{g}\\)) (x). Then evaluate the quotient when x = 5.<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\nLet f(x) = 6x<sup>3<\/sup> and g(x) = 8x<sup>3<\/sup>. Find ( f + g)(x). Then evaluate the sum when x = 2.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46439\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-59.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 a 59\" width=\"347\" height=\"170\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-59.png 347w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-a-59-300x147.png 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><\/p>\n<p>Question 60.<br \/>\nLet f(x) = 2x<sup>x<\/sup> and g(x) = 3x<sup>x<\/sup>. Find ( f &#8211; g)(x). Then evaluate the difference when x = 6.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Exponential_and_Logarithmic_Functions_Study_Skills:_Forming_a_Weekly_Study_Group\"><\/a>Exponential and Logarithmic Functions Study Skills: Forming a Weekly Study Group<\/h3>\n<p><strong>6.1\u20136.4 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40287\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-12.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 12\" width=\"573\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-12.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-12-300x55.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p><strong>Core Concepts<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-13.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 13\" width=\"684\" height=\"293\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-13.png 684w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-13-300x129.png 300w\" sizes=\"(max-width: 684px) 100vw, 684px\" \/><\/p>\n<p><strong>Mathematical Practices<\/strong><br \/>\nQuestion 1.<br \/>\nHow did you check to make sure your answer was reasonable in Exercise 23 on page 300?<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nHow can you justify your conclusions in Exercises 23\u201326 on page 307?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nHow did you monitor and evaluate your progress in Exercise 66 on page 315?<br \/>\nAnswer:<\/p>\n<p><strong>Study Skills: Forming a Weekly Study Group<\/strong><\/p>\n<ul>\n<li>Select students who are just as dedicated to doing well in the math class as you are.<\/li>\n<li>ind a regular meeting place that has minimal distractions.<\/li>\n<li>Compare schedules and plan at least one time a week to meet, allowing at least 1.5 hours for study time.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40289\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-14.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.4 14\" width=\"363\" height=\"269\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-14.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.4-14-300x222.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/li>\n<\/ul>\n<h3><a id=\"Exponential_and_Logarithmic_Functions_6.1\u20136.4_Quiz\"><\/a>Exponential and Logarithmic Functions 6.1\u20136.4 Quiz<\/h3>\n<p>Tell whether the function represents exponential growth or exponential decay. Explain your reasoning.<br \/>\nQuestion 1.<br \/>\nf(x) = (4.25)<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ny = (\\(\\frac{3}{8}\\))<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\ny = e<sup>0.6x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nf(x) = 5e<sup>-2x<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 5.<br \/>\ne<sup>8<\/sup> \u2022 e<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{15 e^{3}}{3 e}\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n(5e<sup>4x<\/sup>)<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nel<sup>ln 9<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nlog<sub>7<\/sub> 49<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nlog<sub>3<\/sub> 81<sup>-2x<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>Rewrite the expression in exponential or logarithmic form.<\/strong><br \/>\nQuestion 11.<br \/>\nlog<sub>4<\/sub> 1024 = 5<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nlog<sub>1\/3<\/sub> 27 = \u22123<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n7<sup>4<\/sup> = 2401<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n4<sup>-2<\/sup> = 0.0625<br \/>\nAnswer:<\/p>\n<p><strong>Evaluate the logarithm. If necessary, use a calculator and round your answer to three decimal places.<\/strong><br \/>\nQuestion 15.<br \/>\nlog 45<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\nln 1.4<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nlog<sub>2<\/sub> 32<br \/>\nAnswer:<\/p>\n<p><strong>Graph the function and its inverse.<\/strong><br \/>\nQuestion 18.<br \/>\nf(x) = (\\(\\frac{1}{9}\\))<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\ny = ln(x \u2212 7)<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\nf(x) = log<sub>5<\/sub> (x+ 1)<br \/>\nAnswer:<\/p>\n<p><strong>The graph of g is a transformation of the graph of f. Write a rule for g.<\/strong><br \/>\nQuestion 21.<br \/>\nf(x) = log<sub>3<\/sub> x<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40290\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-q-1.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions q 1\" width=\"160\" height=\"137\" \/><br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\nf(x) = 3<sup>x<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40291\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-q-2.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions q 2\" width=\"154\" height=\"129\" \/><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nf(x)= log<sub>1\/2<\/sub> x<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-q-3.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions q 3\" width=\"149\" height=\"135\" \/><br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\nYou purchase an antique lamp for $150. The value of the lamp increases by 2.15% each year. Write an exponential model that gives the value y (in dollars) of the lamp t years after you purchased it.<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\nA local bank advertises two certificate of deposit (CD) accounts that you can use to save money and earn interest. The interest is compounded monthly for both accounts.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40293\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-q-4.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions q 4\" width=\"247\" height=\"183\" \/><br \/>\na. You deposit the minimum required amounts in each CD account. How much money is in each account at the end of its term? How much interest does each account earn? Justify your answers.<br \/>\nb. Describe the benefits and drawbacks of each account.<br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\nThe Richter scale is used for measuring the magnitude of an earthquake. The Richter magnitude R is given by R = 0.67 ln E + 1.17, where E is the energy (in kilowatt-hours) released by the earthquake. Graph the model. What is the Richter magnitude for an earthquake that releases 23,000 kilowatt-hours of energy?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_6.5_Properties_of_Logarithms\"><\/a>Lesson 6.5 Properties of Logarithms<\/h3>\n<p><strong>Essential Question<\/strong> How can you use properties of exponents to derive properties of logarithms?<br \/>\nLet x = log<sub>b<\/sub> m and y = log<sub>b<\/sub> n.<br \/>\nThe corresponding exponential forms of these two equations are<br \/>\nb<sup>x<\/sup> = m and b<sup>y<\/sup> = n.<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Product Property of Logarithms<br \/>\nWork with a partner. To derive the Product Property, multiply m and n to obtain mn =b<sup>x<\/sup>b<sup>y<\/sup> = b<sup>x+y<\/sup>.<br \/>\nThe corresponding logarithmic form of mn = b<sup>x+y<\/sup> is log<sub>b<\/sub> mn = x + y. So,<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40294\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-1.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 1\" width=\"653\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-1.png 653w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-1-300x85.png 300w\" sizes=\"(max-width: 653px) 100vw, 653px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Quotient Property of Logarithms<br \/>\nWork with a partner. To derive the Quotient Property, divide m by n to obtain<br \/>\n\\(\\frac{m}{n}=\\frac{b^{x}}{b^{y}}\\) = b<sup>x-y<\/sup>.<br \/>\nThe corresponding logarithmic form of \\(\\frac{m}{n}\\) = b<sup>x-y<\/sup> is log<sub>b<\/sub> \\(\\frac{m}{n}\\) = x \u2212 y. So,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40295\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-2.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 2\" width=\"482\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-2.png 482w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-2-300x41.png 300w\" sizes=\"(max-width: 482px) 100vw, 482px\" \/><\/p>\n<p><strong>EXPLORATION 3<\/strong><\/p>\n<p>Power Property of Logarithms<br \/>\nWork with a partner. To derive the Power Property, substitute b<sup>x<\/sup> for m in the expression log<sub>b<\/sub> m<sup>n<\/sup>, as follows.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40296\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-3.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 3\" width=\"589\" height=\"156\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-3.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-3-300x79.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 4.<br \/>\nHow can you use properties of exponents to derive properties of logarithms?<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nUse the properties of logarithms that you derived in Explorations 1\u20133 to evaluate each logarithmic expression.<br \/>\na. log<sub>4<\/sub> 16<sup>3<\/sup><br \/>\nb. log<sub>3<\/sub> 81<sup>-3<\/sup><br \/>\nc. ln e<sup>2<\/sup> + ln e<sup>5<\/sup><br \/>\nd. 2 ln e<sup>6<\/sup> \u2212 ln e<sup>5<\/sup><br \/>\ne. log<sub>5<\/sub> 75 \u2212 log<sub>5<\/sub> 3<br \/>\nf. log<sub>4<\/sub> 2 + log<sub>4<\/sub> 32<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Use log<sub>6<\/sub> 5 \u2248 0.898 and log<sub>6<\/sub> 8 \u2248 1.161 to evaluate the logarithm.<\/strong><br \/>\nQuestion 1.<br \/>\nlog<sub>6<\/sub> \\(\\frac{5}{8}\\)<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nlog<sub>6<\/sub> 40<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nlog<sub>6<\/sub> 64<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nlog<sub>6<\/sub> 125<br \/>\nAnswer:<\/p>\n<p><strong>Expand the logarithmic expression.<\/strong><br \/>\nQuestion 5.<br \/>\nlog<sub>6<\/sub> 3x<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nln \\(\\frac{5}{12x}\\)<br \/>\nAnswer:<\/p>\n<p><strong>Condense the logarithmic expression.<\/strong><br \/>\nQuestion 7.<br \/>\nlog x \u2212 log 9<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nln 4 + 3 ln 3 \u2212 ln 12<br \/>\nAnswer:<\/p>\n<p><strong>Use the change-of-base formula to evaluate the logarithm.<\/strong><br \/>\nQuestion 9.<br \/>\nlog<sub>5<\/sub> 8<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nlog<sub>8<\/sub> 14<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nlog<sub>26<\/sub> 9<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nlog<sub>12<\/sub> 30<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 6, the artist turns up the volume so that the intensity of the sound triples. By how many decibels does the loudness increase?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Properties_of_Logarithms_6.5_Exercises\"><\/a>Properties of Logarithms 6.5 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nTo condense the expression log<sub>3<\/sub> 2x + log<sub>3<\/sub> y, you need to use the __________ Property of Logarithms.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46440\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-1.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 1\" width=\"563\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-1.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-1-300x31.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe two ways to evaluate log7 12 using a calculator.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20138, use log<sub>7<\/sub> 4 \u2248 0.712 and log<sub>7<\/sub> 12 \u2248 1.277 to evaluate the logarithm.<\/strong><br \/>\nQuestion 3.<br \/>\nlog<sub>7<\/sub> 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46441\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-3.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 3\" width=\"251\" height=\"135\" \/><\/p>\n<p>Question 4.<br \/>\nlog<sub>7<\/sub> 48<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nlog<sub>7<\/sub> 16<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46442\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-5.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 5\" width=\"301\" height=\"98\" \/><\/p>\n<p>Question 6.<br \/>\nlog<sub>7<\/sub> 64<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nlog<sub>7<\/sub> \\(\\frac{1}{4}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46443\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-7.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 7\" width=\"291\" height=\"101\" \/><\/p>\n<p>Question 8.<br \/>\nlog<sub>7<\/sub> \\(\\frac{1}{3}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 9\u201312, match the expression with the logarithm that has the same value. Justify your answer.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40297\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-4.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 4\" width=\"298\" height=\"133\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46444\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-9.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 9\" width=\"565\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-9.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-9-300x48.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46445\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-11.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 11\" width=\"468\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-11.png 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-11-300x58.png 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p><strong>In Exercises 13\u201320, expand the logarithmic expression.<\/strong><br \/>\nQuestion 13.<br \/>\nlog<sub>3<\/sub> 4x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46446\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-13.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 13\" width=\"246\" height=\"39\" \/><\/p>\n<p>Question 14.<br \/>\nlog<sub>8<\/sub> 3x<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nlog 10x<sup>5<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46447\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-15.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 15\" width=\"261\" height=\"69\" \/><\/p>\n<p>Question 16.<br \/>\nln 3x<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nln \\(\\frac{x}{3 y}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46448\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-17.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 17\" width=\"252\" height=\"76\" \/><\/p>\n<p>Question 18.<br \/>\nln \\(\\frac{6 x^{2}}{y^{4}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nlog<sub>7<\/sub> 5\\(\\sqrt{x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46449\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-19.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 19\" width=\"420\" height=\"94\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-19.png 420w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-19-300x67.png 300w\" sizes=\"(max-width: 420px) 100vw, 420px\" \/><\/p>\n<p>Question 20.<br \/>\nlog<sub>5<\/sub> \\(\\sqrt[3]{x^{2} y}\\)<br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 21 and 22, describe and correct the error in expanding the logarithmic expression.<br \/>\nQuestion 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40298\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-5.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 5\" width=\"272\" height=\"107\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46450\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-21.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 21\" width=\"543\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-21.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-21-300x54.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40299\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-6.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 6\" width=\"245\" height=\"109\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 23\u201330, condense the logarithmic expression.<\/strong><br \/>\nQuestion 23.<br \/>\nlog<sub>4<\/sub> 7 \u2212 log<sub>4<\/sub> 10<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46451\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-23.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 23\" width=\"270\" height=\"57\" \/><\/p>\n<p>Question 24.<br \/>\nln 12 \u2212 ln 4<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n6 ln x+ 4 ln y<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46452\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-25.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 25\" width=\"387\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-25.png 387w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-25-300x26.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><\/p>\n<p>Question 26.<br \/>\n2 log x+ log 11<br \/>\nans;<\/p>\n<p>Question 27.<br \/>\nlog<sub>5<\/sub> 4 + \\(\\frac{1}{3}\\) log<sub>5<\/sub> x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46453\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-27.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 27\" width=\"475\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-27.png 475w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-27-300x37.png 300w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><\/p>\n<p>Question 28.<br \/>\n6 ln 2 \u2212 4 ln y<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n5 ln 2 + 7 ln x + 4 ln y<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46454\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-29.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 29\" width=\"468\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-29.png 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-29-300x37.png 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 30.<br \/>\nlog<sub>3<\/sub> 4 + 2 log<sub>3<\/sub> \\(\\frac{1}{2}\\) + log<sub>3<\/sub> x<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhich of the following is not equivalent to log<sub>3<\/sub> \\(\\frac{y^{4}}{3 x}\\)? Justify your answer.<br \/>\nA. 4 log<sub>5<\/sub> y \u2212 log<sub>5<\/sub> 3x<br \/>\nB. 4 log<sub>5<\/sub> y \u2212 log<sub>5<\/sub> 3 + log<sub>5<\/sub> x<br \/>\nC. 4 log<sub>5<\/sub> y\u2212 log<sub>5<\/sub> 3 \u2212 log<sub>5<\/sub> x<br \/>\nD. log<sub>5<\/sub> y<sup>4<\/sup> \u2212 log<sub>5<\/sub> 3 \u2212 log<sub>5<\/sub> x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46455\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-31.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 31\" width=\"569\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-31.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-31-300x107.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhich of the following equations is correct? Justify your answer.<br \/>\nA. log<sub>7<\/sub> x + 2 log<sub>7<\/sub> y = log<sub>7<\/sub> (x + y<sup>2<\/sup>)<br \/>\nB. 9 log x \u2212 2 log y = log \\(\\frac{x^{9}}{y^{2}}\\)<br \/>\nC. 5 log<sub>4<\/sub> x + 7 log<sub>2<\/sub> y = log<sub>6<\/sub>x<sup>5<\/sup>y<sup>7<\/sup><br \/>\nD. log<sub>9<\/sub>x \u2212 5 log<sub>9<\/sub> y = log<sub>9<\/sub> \\(\\frac{x}{5 y}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 33\u201340, use the change-of-base formula to evaluate the logarithm.<\/strong><br \/>\nQuestion 33.<br \/>\nlog<sub>4<\/sub> 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46456\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-33.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 33\" width=\"229\" height=\"58\" \/><\/p>\n<p>Question 34.<br \/>\nlog<sub>5<\/sub> 13<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\nlog<sub>9<\/sub> 15<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46457\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-35.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 35\" width=\"251\" height=\"61\" \/><\/p>\n<p>Question 36.<br \/>\nlog<sub>8<\/sub> 22<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\nlog<sub>6<\/sub> 17<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46458\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-37.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 37\" width=\"242\" height=\"57\" \/><\/p>\n<p>Question 38.<br \/>\nlog<sub>2<\/sub> 28<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\nlog<sub>7<\/sub> \\(\\frac{3}{16}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46459\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-39.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 39\" width=\"274\" height=\"71\" \/><\/p>\n<p>Question 40.<br \/>\nlog<sub>3<\/sub> \\(\\frac{9}{40}\\)<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims you can use the change-of-base formula to graph y = log<sub>3<\/sub>x using a graphing calculator. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46460\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-41.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 41\" width=\"552\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-41.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-41-300x48.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the graph to determine the value of \\(\\frac{\\log 8}{\\log 2}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40300\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-7.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 7\" width=\"164\" height=\"105\" \/><br \/>\nAnswer:<\/p>\n<p><strong>MODELING WITH MATHEMATICS<\/strong> In Exercises 43 and 44, use the function L(I ) given in Example 6.<br \/>\nQuestion 43.<br \/>\nThe blue whale can produce sound with an intensity that is 1 million times greater than the intensity of the loudest sound a human can make. Find the difference in the decibel levels of the sounds made by a blue whale and a human.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40301\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-8.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 8\" width=\"251\" height=\"144\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46461\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-43.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 43\" width=\"576\" height=\"419\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-43.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-43-300x218.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 44.<br \/>\nThe intensity of the sound of a certain television advertisement is 10 times greater than the intensity of the television program. By how many decibels does the loudness increase?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40302\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-9.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 9\" width=\"318\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-9.png 318w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-9-300x157.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>REWRITING A FORMULA<\/strong><br \/>\nUnder certain conditions, the wind speed s (in knots) at an altitude of h meters above a grassy plain can be modeled by the function s(h) = 2 ln 100h.<br \/>\na. By what amount does the wind speed increase when the altitude doubles?<br \/>\nb. Show that the given function can be written in terms of common logarithms as<br \/>\ns(h) = \\(\\frac{2}{\\log e}\\)(log h+ 2).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46462\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-45.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 45\" width=\"585\" height=\"549\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-45.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-45-300x282.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nDetermine whether the formula<br \/>\nlog<sub>b<\/sub> (M + N) = log<sub>b<\/sub> M + log<sub>b<\/sub>N<br \/>\nis true for all positive, real values of M, N, and b(with b\u2260 1). Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nUse the properties of exponents to prove the change-of-base formula. (Hint: Let x= log<sub>b<\/sub> a, y = log<sub>b<\/sub> c, and z = log<sub>b<\/sub> a.)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46463\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-47.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 47\" width=\"583\" height=\"150\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-47.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-47-300x77.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nDescribe three ways to transform the graph of f(x) = log x to obtain the graph of g(x) = log 100x \u2212 1. Justify your answers.<br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Solve the inequality by graphing.<\/strong><br \/>\nQuestion 49.<br \/>\nx<sup>2<\/sup> \u2212 4 &gt; 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46464\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-49.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 49\" width=\"563\" height=\"622\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-49.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-49-272x300.png 272w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 50.<br \/>\n2(x \u2212 6)<sup>2<\/sup> \u2212 5 \u2265 37<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\nx<sup>2<\/sup> + 13x + 42 &lt; 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46465\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-51.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 51\" width=\"572\" height=\"634\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-51.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-51-271x300.png 271w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 52.<br \/>\n\u2212x<sup>2<\/sup> \u2212 4x + 6 \u2264 \u22126<br \/>\nAnswer:<\/p>\n<p><strong>Solve the equation by graphing the related system of equations.<\/strong><br \/>\nQuestion 53.<br \/>\n4x<sup>2<\/sup> \u2212 3x \u2212 6 = \u2212x<sup>2<\/sup> + 5x + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46466\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-53.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 53\" width=\"566\" height=\"498\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-53.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-53-300x264.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 54.<br \/>\n\u2212(x + 3)(x \u2212 2) = x<sup>2<\/sup> \u2212 6x<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n2x<sup>2<\/sup> \u2212 4x \u2212 5 = \u2212(x + 3)<sup>2<\/sup> + 10<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46467\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-55.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 6 Exponential and Logarithmic Functions 6.5 a 55\" width=\"570\" height=\"498\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-55.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-6.5-a-55-300x262.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 56.<br \/>\n\u2212(x + 7)<sup>2<\/sup> + 5 = (x + 10)<sup>2<\/sup> \u2212 3<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_6.6_Solving_Exponential_and_Logarithmic_Equations\"><\/a>Lesson 6.6 Solving Exponential and Logarithmic Equations<\/h3>\n<p><strong>Essential Question<\/strong> How can you solve exponential and logarithmic equations?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Solving Exponential and Logarithmic Equations<br \/>\nWork with a partner. Match each equation with the graph of its related system of equations. Explain your reasoning. Then use the graph to solve the equation.<br \/>\na. e<sup>x<\/sup> = 2<br \/>\nb. ln x = \u22121<br \/>\nc. 2<sup>x<\/sup> = 3<sup>-x<\/sup><br \/>\nd. log<sub>4<\/sub>x = 1<br \/>\ne. log<sub>5<\/sub> x = \\(\\frac{1}{2}\\)<br \/>\nf. 4<sup>x<\/sup> = 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40303\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 1\" width=\"557\" height=\"330\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-1.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-1-300x178.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Solving Exponential and Logarithmic Equations<br \/>\nWork with a partner. Look back at the equations in Explorations 1(a) and 1(b). Suppose you want a more accurate way to solve the equations than using a graphical approach.<br \/>\na. Show how you could use a numerical approach by creating a table. For instance, you might use a spreadsheet to solve the equations.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40304\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 2\" width=\"230\" height=\"164\" \/><br \/>\nb. Show how you could use an analytical approach. For instance, you might try solving the equations by using the inverse properties of exponents and logarithms.<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you solve exponential and logarithmic equations?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nSolve each equation using any method. Explain your choice of method.<br \/>\na. 16<sup>x<\/sup> = 2<br \/>\nb. 2<sup>x<\/sup> = 4<sup>2x+1<\/sup><br \/>\nc. 2<sup>x<\/sup> = 3<sup>x+1<\/sup><br \/>\nd. log x = \\(\\frac{1}{2}\\)<br \/>\ne. ln x = 2<br \/>\nf. log<sub>3<\/sub> x = \\(\\frac{3}{2}\\)<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the equation.<\/strong><br \/>\nQuestion 1.<br \/>\n2<sup>x<\/sup> = 5<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n7<sup>9x<\/sup> = 15<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n4e<sup>-0.3x<\/sup> \u2212 7 = 13<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 2, how long will it take to cool the stew to 100\u00baF when the room temperature is 75\u00baF?<br \/>\nAnswer:<\/p>\n<p><strong>Solve the equation. Check for extraneous solutions.<\/strong><br \/>\nQuestion 5.<br \/>\nln(7x \u2212 4) = ln(2x + 11)<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nlog<sub>2<\/sub>(x \u2212 6) = 5<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nlog 5x + log(x \u2212 1) = 2<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nlog<sub>4<\/sub> (x + 12) + log<sub>4<\/sub> x = 3<br \/>\nAnswer:<\/p>\n<p><strong>Solve the inequality.<\/strong><br \/>\nQuestion 9.<br \/>\ne<sup>x<\/sup> &lt; 2<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n10<sup>2x-6<\/sup> &gt; 3<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nlog x + 9 &lt; 45 Answer: Question 12. 2 ln x \u2212 1 &gt; 4<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Exponential_and_Logarithmic_Equations_6.6_Exercises\"><\/a>Solving Exponential and Logarithmic Equations 6.6 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe equation 3<sup>x-1<\/sup> = 34 is an example of a(n) ___________ equation.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46470\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 1\" width=\"533\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-1.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-1-300x35.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare the methods for solving exponential and logarithmic equations.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<strong>WRITING<\/strong><br \/>\nWhen do logarithmic equations have extraneous solutions?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46471\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 3\" width=\"587\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-3.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-3-300x42.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nIf b is a positive real number other than 1, then b<sup>x<\/sup> = b<sup>y<\/sup> if and only if _________<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 5\u201316, solve the equation.<\/strong><br \/>\nQuestion 5.<br \/>\n7<sup>3x+5<\/sup> = 7<sup>1-x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46472\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-5.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 5\" width=\"177\" height=\"167\" \/><\/p>\n<p>Question 6.<br \/>\ne<sup>2x<\/sup> = e<sup>3x-1<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n5<sup>x-3<\/sup> = 25<sup>x-5<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46473\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-7.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 7\" width=\"196\" height=\"236\" \/><\/p>\n<p>Question 8.<br \/>\n6<sup>2x-6<\/sup> = 36<sup>3x-5<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n3<sup>x<\/sup> = 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46474\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-9.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 9\" width=\"166\" height=\"133\" \/><\/p>\n<p>Question 10.<br \/>\n5<sup>x<\/sup> = 33<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n49<sup>5x+2<\/sup> = (\\(\\frac{1}{7}\\))<sup>11-x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46475\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-11.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 11\" width=\"241\" height=\"291\" \/><\/p>\n<p>Question 12.<br \/>\n512<sup>5x-1<\/sup> = (\\(\\frac{1}{8}\\))<sup>-4-x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n7<sup>5x<\/sup> = 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46476\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-13.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 13\" width=\"203\" height=\"183\" \/><\/p>\n<p>Question 14.<br \/>\n11<sup>6x<\/sup> = 38<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n3e<sup>4x+9<\/sup> = 15<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46477\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-15.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 15\" width=\"186\" height=\"258\" \/><\/p>\n<p>Question 16.<br \/>\n2e<sup>2x<\/sup> \u2212 7 = 5<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe length \u2113(in centimeters) of a scalloped hammerhead shark can be modeled by the function \u2113 = 266 \u2212 219<sup>-0.05t<\/sup><br \/>\nwhere t is the age (in years) of the shark. How old is a shark that is 175 centimeters long?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40305\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 3\" width=\"301\" height=\"144\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46478\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-17.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 17\" width=\"322\" height=\"277\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-17.png 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-17-300x258.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><\/p>\n<p>Question 18.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nOne hundred grams of radium are stored in a container. The amount R(in grams) of radium present after t years can be modeled by R= 100e<sup>\u22120.00043t<\/sup>. After how many years will only 5 grams of radium be present?<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 19 and 20, use Newton\u2019s Law of Cooling to solve the problem.<\/strong><br \/>\nQuestion 19.<br \/>\nYou are driving on a hot day when your car overheats and stops running. The car overheats at 280\u00b0F and can be driven again at 230\u00b0F. When it is 80\u00b0F outside, the cooling rate of the car is r = 0.0058. How long do you have to wait until you can continue driving?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40306\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-4.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 4\" width=\"218\" height=\"140\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46479\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-19.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 19\" width=\"579\" height=\"385\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-19.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-19-300x199.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 20.<br \/>\nYou cook a turkey until the internal temperature reaches 180\u00b0F. The turkey is placed on the table until the internal temperature reaches 100\u00b0F and it can be carved. When the room temperature is 72\u00b0F, the cooling rate of the turkey is r = 0.067. How long do you have to wait until you can carve the turkey?<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 21\u201332, solve the equation.<\/strong><br \/>\nQuestion 21.<br \/>\nln(4x \u2212 7) = ln(x + 11)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46480\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-21.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 21\" width=\"554\" height=\"168\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-21.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-21-300x91.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 22.<br \/>\nln(2x \u2212 4) = ln(x + 6)<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nlog<sub>2<\/sub>(3x \u2212 4) = log<sub>2<\/sub> 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46481\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-23.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 23\" width=\"557\" height=\"138\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-23.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-23-300x74.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 24.<br \/>\nlog(7x + 3) = log 38<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\nlog<sub>2<\/sub>(4x + 8) = 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46482\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-25.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 25\" width=\"519\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-25.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-25-300x96.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 26.<br \/>\nlog<sub>3<\/sub>(2x + 1) = 2<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nlog<sub>7<\/sub>(4x + 9) = 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46483\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-27.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 27\" width=\"525\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-27.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-27-300x95.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 28.<br \/>\nlog<sub>5<\/sub>(5x + 10) = 4<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nlog(12x \u2212 9) = log 3x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46484\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-29.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 29\" width=\"559\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-29.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-29-300x110.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 30.<br \/>\nlog<sub>6<\/sub>(5x + 9) = log<sub>6<\/sub> 6x<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\nlog<sub>2<\/sub>(x<sup>2<\/sup> \u2212 x \u2212 6) = 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46485\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-31.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 31\" width=\"403\" height=\"554\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-31.png 403w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-31-218x300.png 218w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/p>\n<p>Question 32.<br \/>\nlog<sub>3<\/sub>(x<sup>2<\/sup> + 9x + 27) = 2<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 33\u201340, solve the equation. Check for extraneous solutions.<\/strong><br \/>\nQuestion 33.<br \/>\nlog<sub>2<\/sub> x + log<sub>2<\/sub> (x \u2212 2) = 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46486\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-33.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 33\" width=\"534\" height=\"629\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-33.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-33-255x300.png 255w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Question 34.<br \/>\nlog<sub>6<\/sub> 3x + log<sub>6<\/sub> (x \u2212 1) = 3<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\nln x + ln(x + 3) = 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46487\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-35.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 35\" width=\"584\" height=\"521\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-35.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-35-300x268.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 36.<br \/>\nln x + ln(x \u2212 2) = 5<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\nlog<sub>3<\/sub> 3x<sup>2<\/sup> + log<sub>3<\/sub> 3 = 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46488\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-37.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 37\" width=\"371\" height=\"599\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-37.png 371w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-37-186x300.png 186w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><\/p>\n<p>Question 38.<br \/>\nlog<sub>4<\/sub> (\u2212x) + log<sub>4<\/sub> (x + 10) = 2<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\nlog<sub>3<\/sub>(x \u2212 9) + log<sub>3<\/sub>(x \u2212 3) = 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46489\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-39.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 39\" width=\"551\" height=\"552\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-39.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-39-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-39-150x150.png 150w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 40.<br \/>\nlog<sub>5<\/sub> (x + 4) + log<sub>5<\/sub> (x + 1) = 2<br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 41 and 42, describe and correct the error in solving the equation.<br \/>\nQuestion 41.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40307\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-5.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 5\" width=\"315\" height=\"145\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-5.png 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-5-300x138.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46490\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-41.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 41\" width=\"584\" height=\"231\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-41.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-41-300x119.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 42.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40308\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-6.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 6\" width=\"319\" height=\"190\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-6.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-6-300x179.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou deposit $100 in an account that pays 6% annual interest. How long will it take for the balance to reach $1000 for each frequency of compounding?<br \/>\na. annual<br \/>\nb. quarterly<br \/>\nc. daily<br \/>\nd. continuously<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46491\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-43.1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 43.1\" width=\"294\" height=\"600\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-43.1.png 294w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-43.1-147x300.png 147w\" sizes=\"(max-width: 294px) 100vw, 294px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46492\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-43.2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 43.2\" width=\"332\" height=\"582\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-43.2.png 332w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-43.2-171x300.png 171w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe apparent magnitude of a star is a measure of the brightness of the star as it appears to observers on Earth. The apparent magnitude M of the dimmest star that can be seen with a telescope is M = 5 log D+ 2, where D is the diameter (in millimeters) of the telescope\u2019s objective lens. What is the diameter of the objective lens of a telescope that can reveal stars with a magnitude of 12?<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nApproximate the solution of each equation using the graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40309\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-7.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 7\" width=\"317\" height=\"192\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-7.png 317w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-7-300x182.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46493\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-45.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 45\" width=\"401\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-45.png 401w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-45-300x47.png 300w\" sizes=\"(max-width: 401px) 100vw, 401px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend states that a logarithmic equation cannot have a negative solution because logarithmic functions are not defined for negative numbers. Is your friend correct? Justify your answer.<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 47\u201354, solve the inequality.<\/strong><br \/>\nQuestion 47.<br \/>\n9<sup>x<\/sup> &gt; 54<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46494\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-47.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 47\" width=\"533\" height=\"201\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-47.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-47-300x113.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Question 48.<br \/>\n4<sup>x<\/sup> \u2264 36<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\nln x \u2265 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46495\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-49.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 49\" width=\"566\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-49.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-49-300x85.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 50.<br \/>\nlog<sub>4<\/sub> x&lt; 4<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n3<sup>4x-5<\/sup> &lt; 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46496\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-51.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 51\" width=\"642\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-51.png 642w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-51-300x133.png 300w\" sizes=\"(max-width: 642px) 100vw, 642px\" \/><\/p>\n<p>Question 52.<br \/>\ne<sup>3x+4<\/sup> &gt; 11<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n\u22123 log<sub>5<\/sub> x + 6 \u2264 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46497\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-53.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 53\" width=\"214\" height=\"238\" \/><\/p>\n<p>Question 54.<br \/>\n\u22124 log<sub>5<\/sub> x \u2212 5 \u2265 3<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<strong>COMPARING METHODS<\/strong><br \/>\nSolve log<sub>5<\/sub> x&lt; 2 algebraically and graphically. Which method do you prefer? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46498\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-55.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 55\" width=\"548\" height=\"369\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-55.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-55-300x202.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou deposit $1000 in an account that pays 3.5% annual interest compounded monthly. When is your balance at least $1200? $3500?<br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nAn investment that earns a rate of return r doubles in value in t years, where t = \\(\\frac{\\ln 2}{\\ln (1+r)}\\) and r is expressed as a decimal. What rates of return will double the value of an investment in less than 10 years?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46499\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-57.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 57\" width=\"403\" height=\"321\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-57.png 403w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-57-300x239.png 300w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/p>\n<p>Question 58.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYour family purchases a new car for $20,000. Its value decreases by 15% each year. During what interval does the car\u2019s value exceed $10,000?<br \/>\nAnswer:<\/p>\n<p><strong>USING TOOLS<\/strong> In Exercises 59\u201362, use a graphing calculator to solve the equation.<br \/>\nQuestion 59.<br \/>\nln 2x = 3<sup>-x+2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46500\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-59.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 59\" width=\"489\" height=\"194\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-59.png 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-59-300x119.png 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><\/p>\n<p>Question 60.<br \/>\nlog x = 7<sup>-x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\nlog x = 3<sup>x-3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46501\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-61.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 61\" width=\"439\" height=\"196\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-61.png 439w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-61-300x134.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><\/p>\n<p>Question 62.<br \/>\nln 2x = e<sup>x-3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n<strong>REWRITING A FORMULA<\/strong><br \/>\nA biologist can estimate the age of an African elephant by measuring the length of its footprint and using the equation \u2113 = 45 \u2212 25.7e<sup>\u22120.09a<\/sup>, where \u2113is the length (in centimeters) of the footprint and a is the age (in years).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40310\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-8.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 8\" width=\"144\" height=\"258\" \/><br \/>\na. Rewrite the equation, solving for a in terms of \u2113.<br \/>\nb. Use the equation in part (a) to find the ages of the elephants whose footprints are shown.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46502\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-63.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 63\" width=\"403\" height=\"665\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-63.png 403w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-63-182x300.png 182w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/p>\n<p>Question 64.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the graph to solve the inequality 4 ln x + 6 &gt; 9. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40311\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-9.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 9\" width=\"198\" height=\"103\" \/><br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite an exponential equation that has a solution of x = 4. Then write a logarithmic equation that has a solution of x = \u22123.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46503\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-65.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 65\" width=\"462\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-65.png 462w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-65-300x46.png 300w\" sizes=\"(max-width: 462px) 100vw, 462px\" \/><\/p>\n<p>Question 66.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nGive examples of logarithmic or exponential equations that have one solution, two solutions, and no solutions.<br \/>\nAnswer:<\/p>\n<p><strong>CRITICAL THINKING<\/strong> In Exercises 67\u201372, solve the equation.<br \/>\nQuestion 67.<br \/>\n2<sup>x+3<\/sup> = 5<sup>3x-1<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46504\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-67.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 67\" width=\"630\" height=\"358\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-67.png 630w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-67-300x170.png 300w\" sizes=\"(max-width: 630px) 100vw, 630px\" \/><\/p>\n<p>Question 68.<br \/>\n10<sup>3x-8<\/sup> = 2<sup>5-x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 69.<br \/>\nlog<sub>3<\/sub> (x \u2212 6) = log<sub>9<\/sub> 2x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46505\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-69.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 69\" width=\"519\" height=\"327\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-69.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-69-300x189.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 70.<br \/>\nlog<sub>4<\/sub> x = log<sub>8<\/sub> 4x<br \/>\nAnswer:<\/p>\n<p>Question 71.<br \/>\n2<sup>2x<\/sup> \u2212 12 \u2022 2<sup>x<\/sup> + 32 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46506\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-71.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 71\" width=\"487\" height=\"333\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-71.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-71-300x205.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><\/p>\n<p>Question 72.<br \/>\n5<sup>2x<\/sup> + 20 \u2022 5<sup>x<\/sup> \u2212 125 = 0<br \/>\nAnswer:<\/p>\n<p>Question 73.<br \/>\n<strong>WRITING<\/strong><br \/>\nIn Exercises 67\u201370, you solved exponential and logarithmic equations with different bases. Describe general methods for solving such equations.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46507\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-73.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 73\" width=\"581\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-73.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-73-300x114.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 74.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nWhen X-rays of a fixed wavelength strike a material x centimeters thick, the intensity I(x) of the X-rays transmitted through the material is given by I(x) = I<sub>0<\/sub>e<sup>\u2212\u03bcx<\/sup>, where I0 is the initial intensity and \u03bc is a value that depends on the type of material and the wavelength of the X-rays. The table shows the values of \u03bc for various materials and X-rays of medium wavelength.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40312\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-10.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 10\" width=\"291\" height=\"76\" \/><br \/>\na. Find the thickness of aluminum shielding that reduces the intensity of X-rays to 30% of their initial intensity. (Hint: Find the value of x for which I(x) = 0.3I<sub>0<\/sub>.)<br \/>\nb. Repeat part (a) for the copper shielding.<br \/>\nc. Repeat part (a) for the lead shielding.<br \/>\nd. Your dentist puts a lead apron on you before taking X-rays of your teeth to protect you from harmful radiation. Based on your results from parts (a)\u2013(c), explain why lead is a better material to use than aluminum or copper.<br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Write an equation in point-slope form of the line that passes through the given point and has the given slope.<\/strong><br \/>\nQuestion 75.<br \/>\n(1, \u22122); m = 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46508\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-75.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 75\" width=\"245\" height=\"130\" \/><\/p>\n<p>Question 76.<br \/>\n(3, 2); m = \u22122<br \/>\nAnswer:<\/p>\n<p>Question 77.<br \/>\n(3, \u22128); m = \u2212 \\(\\frac{1}{3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46509\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-77.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 77\" width=\"233\" height=\"170\" \/><\/p>\n<p>Question 78.<br \/>\n(2, 5); m = 2<br \/>\nAnswer:<\/p>\n<p>Use finite differences to determine the degree of the polynomial function that fits the data. Then use technology to find the polynomial function.<br \/>\nQuestion 79.<br \/>\n(\u22123, \u221250), (\u22122, \u221213), (\u22121, 0), (0, 1), (1, 2), (2, 15), (3, 52), (4, 125)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46510\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-79.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 79\" width=\"590\" height=\"196\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-79.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-79-300x100.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 80.<br \/>\n(\u22123, 139), (\u22122, 32), (\u22121, 1), (0, \u22122), (1, \u22121), (2, 4), (3, 37), (4, 146)<br \/>\nAnswer:<\/p>\n<p>Question 81.<br \/>\n(\u22123, \u2212327), (\u22122, \u221284), (\u22121, \u221217), (0, \u22126), (1, \u22123), (2, \u221232), (3, \u2212189), (4, \u2212642)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46511\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-81.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 6 Exponential and Logarithmic Functions 6.6 a 81\" width=\"517\" height=\"281\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-81.png 517w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-6-Exponential-and-Logarithmic-Functions-6.6-a-81-300x163.png 300w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><\/p>\n<h3><a id=\"Lesson_6.7_Modeling_with_Exponential_and_Logarithmic_Functions\"><\/a>Lesson 6.7 Modeling with Exponential and Logarithmic Functions<\/h3>\n<p><strong>Essential Question<\/strong> How can you recognize polynomial, exponential, and logarithmic models?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Recognizing Different Types of Models<br \/>\nWork with a partner. Match each type of model with the appropriate scatter plot. Use a regression program to find a model that fits the scatter plot.<br \/>\na. linear (positive slope)<br \/>\nb. linear (negative slope)<br \/>\nc. quadratic<br \/>\nd. cubic<br \/>\ne. exponential<br \/>\nf. logarithmic<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40313\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 1\" width=\"444\" height=\"447\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-1.png 444w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-1-298x300.png 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-1-150x150.png 150w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Exploring Gaussian and Logistic Models<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40314\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 2\" width=\"238\" height=\"188\" \/><br \/>\nWork with a partner. Two common types of functions that are related to exponential functions are given. Use a graphing calculator to graph each function. Then determine the domain, range, intercept, and asymptote(s) of the function.<br \/>\na. Gaussian Function: f(x) = e<sup>\u2212x<sup>2<\/sup><\/sup><br \/>\nb. Logistic Function: f(x) = \\(\\frac{1}{1+e^{-x}}\\)<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you recognize polynomial, exponential, and logarithmic models?<br \/>\nAnswer:<\/p>\n<p>Question4 .<br \/>\nUse the Internet or some other reference to find real-life data that can be modeled using one of the types given in Exploration 1. Create a table and a scatter plot of the data. Then use a regression program to find a model that fits the data.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Determine the type of function represented by the table. Explain your reasoning.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40315\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 3\" width=\"208\" height=\"72\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40316\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-4.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 4\" width=\"213\" height=\"72\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Write an exponential function y = ab<sup>x<\/sup> whose graph passes through the given points.<\/strong><br \/>\nQuestion 3.<br \/>\n(2, 12), (3, 24)<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n(1, 2), (3, 32)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n(2, 16), (5, 2)<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nRepeat Examples 3 and 4 using the sales data from another store.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40317\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 5\" width=\"479\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-5.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-5-300x39.png 300w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nUse a graphing calculator to find an exponential model for the data in Monitoring Progress Question 6.<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nUse a graphing calculator to find a logarithmic model of the form p = a + b ln h for the data in Example 6. Explain why the result is an error message.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Modeling_with_Exponential_and_Logarithmic_Functions_6.7_Exercises\"><\/a>Modeling with Exponential and Logarithmic Functions 6.7 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nGiven a set of more than two data pairs (x, y), you can decide whether a(n) __________ function fits the data well by making a scatter plot of the points (x, ln y).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46512\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 1\" width=\"592\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-1.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-1-300x44.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nGiven a table of values, explain how you can determine whether an exponential function is a good model for a set of data pairs (x, y).<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20136, determine the type of function represented by the table. Explain your reasoning.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40318\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-6.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 6\" width=\"293\" height=\"70\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46513\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 3\" width=\"563\" height=\"269\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-3.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-3-300x143.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40319\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 7\" width=\"326\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-7.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-7-300x65.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40320\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-8.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 8\" width=\"290\" height=\"69\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46514\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 5\" width=\"594\" height=\"353\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-5.png 594w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-5-300x178.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40321\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 9\" width=\"252\" height=\"72\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 7\u201316, write an exponential function y = ab<sup>x<\/sup> whose graph passes through the given points.<\/strong><br \/>\nQuestion 7.<br \/>\n(1, 3), (2, 12)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46515\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 7\" width=\"554\" height=\"447\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-7.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-7-300x242.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 8.<br \/>\n(2, 24), (3, 144)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n(3, 1), (5, 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46516\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 9\" width=\"530\" height=\"419\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-9.png 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-9-300x237.png 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p>Question 10.<br \/>\n(3, 27), (5, 243)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n(1, 2), (3, 50)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46517\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 11\" width=\"514\" height=\"444\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-11.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-11-300x259.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p>Question 12.<br \/>\n(1, 40), (3, 640)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n(\u22121, 10), (4, 0.31)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46518\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 13\" width=\"574\" height=\"401\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-13.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-13-300x210.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 14.<br \/>\n(2, 6.4), (5, 409.6)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40322\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-10.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 10\" width=\"154\" height=\"154\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-10.png 154w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-10-150x150.png 150w\" sizes=\"(max-width: 154px) 100vw, 154px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46519\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 15\" width=\"519\" height=\"448\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-15.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-15-300x259.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40323\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 11\" width=\"154\" height=\"147\" \/><br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 17 and 18, describe and correct the error in determining the type of function represented by the data.<br \/>\nQuestion 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40326\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-12.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 12\" width=\"331\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-12.png 331w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-12-300x146.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46520\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 17\" width=\"580\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-17.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-17-300x47.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40328\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 13\" width=\"331\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-13.png 331w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-13-300x150.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA store sells motorized scooters. The table shows the numbers y of scooters sold during the xth year that the store has been open. Write a function that models the data.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40332\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-14.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 14\" width=\"314\" height=\"227\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-14.png 314w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-14-300x217.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46521\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 19\" width=\"574\" height=\"740\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-19.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-19-233x300.png 233w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe table shows the numbers y of visits to a website during the xth month. Write a function that models the data. Then use your model to predict the number of visits after 1 year.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40334\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 15\" width=\"331\" height=\"64\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-15.png 331w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-15-300x58.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 21\u201324, determine whether the data show an exponential relationship. Then write a function that models the data<\/strong>.<br \/>\nQuestion 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40340\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-16.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 16\" width=\"244\" height=\"71\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46522\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 21\" width=\"581\" height=\"565\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-21.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-21-300x292.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40341\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 17\" width=\"250\" height=\"74\" \/><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40342\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-18.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 18\" width=\"326\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-18.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-18-300x62.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46523\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 23\" width=\"586\" height=\"629\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-23.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-23-279x300.png 279w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40343\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 19\" width=\"286\" height=\"77\" \/><br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYour visual near point is the closest point at which your eyes can see an object distinctly. The diagram shows the near point y (in centimeters) at age x (in years). Create a scatter plot of the data pairs (x, ln y) to show that an exponential model should be a good fit for the original data pairs (x, y). Then write an exponential model for the original data.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40344\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-20.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 20\" width=\"261\" height=\"254\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46524\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-25.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 25.1\" width=\"586\" height=\"550\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-25.1.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-25.1-300x282.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46525\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-25.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 25.2\" width=\"554\" height=\"337\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-25.2.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-25.2-300x182.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nUse the data from Exercise 19. Create a scatter plot of the data pairs (x, ln y) to show that an exponential model should be a good fit for the original data pairs (x, y). Then write an exponential model for the original data.<br \/>\nAnswer:<\/p>\n<p>In Exercises 27\u201330, create a scatter plot of the points (x, ln y) to determine whether an exponential model fits the data. If so, find an exponential model for the data.<br \/>\nQuestion 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40345\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 21\" width=\"232\" height=\"67\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46526\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-27.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 27.1\" width=\"551\" height=\"627\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-27.1.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-27.1-264x300.png 264w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46527\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-27.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 27.2\" width=\"487\" height=\"165\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-27.2.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-27.2-300x102.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40346\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-22.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 22\" width=\"260\" height=\"67\" \/><br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40347\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 23\" width=\"246\" height=\"76\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46528\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 29\" width=\"569\" height=\"758\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-29.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-29-225x300.png 225w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40348\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-24.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 24\" width=\"265\" height=\"68\" \/><br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nUse a graphing calculator to find an exponential model for the data in Exercise 19. Then use the model to predict the number of motorized scooters sold in the tenth year.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46529\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 31\" width=\"574\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-31.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-31-300x57.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nA doctor measures an astronaut\u2019s pulse rate y (in beats per minute) at various times x(in minutes) after the astronaut has finished exercising. The results are shown in the table. Use a graphing calculator to find an exponential model for the data. Then use the model to predict the astronaut\u2019s pulse rate after 16 minutes.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 25\" width=\"308\" height=\"278\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-25.png 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-25-300x271.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nAn object at a temperature of 160\u00b0C is removed from a furnace and placed in a room at 20\u00b0C. The table shows the temperatures d (in degrees Celsius) at selected times t (in hours) after the object was removed from the furnace. Use a graphing calculator to find a logarithmic model of the form t = a +b ln d that represents the data. Estimate how long it takes for the object to cool to 50\u00b0C.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40350\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-26.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 26\" width=\"339\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-26.png 339w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-26-300x59.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46530\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 33\" width=\"573\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-33.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-33-300x57.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nThe f-stops on a camera control the amount of light that enters the camera. Let s be a measure of the amount of light that strikes the film and let f be the f-stop. The table shows several f-stops on a 35-millimeter camera. Use a graphing calculator to find a logarithmic model of the form s = a + b ln f that represents the data. Estimate the amount of light that strikes the film when f = 5.657.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 27\" width=\"329\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-27.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-27-300x157.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nThe table shows the average weight (in kilograms) of an Atlantic cod that is x years old from the Gulf of Maine.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-28.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 28\" width=\"330\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-28.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-28-300x61.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\na. Show that an exponential model fits the data. Then find an exponential model for the data.<br \/>\nb. By what percent does the weight of an Atlantic cod increase each year in this period of time? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46531\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 35\" width=\"609\" height=\"436\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-35.png 609w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-35-300x215.png 300w\" sizes=\"(max-width: 609px) 100vw, 609px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graph shows a set of data points (x, ln y). Do the data pairs (x, y) fit an exponential pattern? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 29\" width=\"196\" height=\"162\" \/><br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says it is possible to find a logarithmic model of the form d = a + b ln t for the data in Exercise 33. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46532\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 37\" width=\"569\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-37.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-37-300x28.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nIs it possible to write y as an exponential function of x? Explain your reasoning. (Assume p is positive.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-30.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 30\" width=\"179\" height=\"168\" \/><br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nYou plant a sunflower seedling in your garden. The height h (in centimeters) of the seedling after t weeks can be modeled by the logistic function<br \/>\nh(t) = \\(\\frac{256}{1+13 e^{-0.65 t}}\\)<br \/>\na. Find the time it takes the sunflower seedling to reach a height of 200 centimeters.<br \/>\nb. Use a graphing calculator to graph the function. Interpret the meaning of the asymptote in the context of this situation.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46533\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 39\" width=\"578\" height=\"636\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-39.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-39-273x300.png 273w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Tell whether x and y are in a proportional relationship. Explain your reasoning.<\/strong><br \/>\nQuestion 40.<br \/>\ny = \\(\\frac{x}{2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\ny = 3x \u2212 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46534\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 41\" width=\"579\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-41.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-41-300x31.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 42.<br \/>\ny = \\(\\frac{5}{x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\ny = \u22122x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46535\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 43\" width=\"586\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-43.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-43-300x31.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Identify the focus, directrix, and axis of symmetry of the parabola. Then graph the equation.<br \/>\nQuestion 44.<br \/>\nx = \\(\\frac{1}{8}\\)y<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\ny = 4x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46536\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-45.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 45\" width=\"536\" height=\"401\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-45.png 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-45-300x224.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Question 46.<br \/>\nx<sup>2<\/sup> = 3y<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\ny<sup>2<\/sup> = \\(\\frac{2}{5}\\)x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46537\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-47.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 a 47\" width=\"605\" height=\"370\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-47.png 605w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-a-47-300x183.png 300w\" sizes=\"(max-width: 605px) 100vw, 605px\" \/><\/p>\n<h3><a id=\"Exponential_and_Logarithmic_Functions_Performance_Task:_Measuring_Natural_Disasters\"><\/a>Exponential and Logarithmic Functions Performance Task: Measuring Natural Disasters<\/h3>\n<p><strong>6.5\u20136.7 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\nexponential equations, p. 334<br \/>\nlogarithmic equations, p. 335<\/p>\n<p><strong>Core Concepts<\/strong><br \/>\nSection 6.5<br \/>\nProperties of Logarithms, p. 328<br \/>\nChange-of-Base Formula, p. 329<\/p>\n<p>Section 6.6<br \/>\nProperty of Equality for Exponential Equations, p. 334<br \/>\nProperty of Equality for Logarithmic Equations, p. 335<\/p>\n<p>Section 6.7<br \/>\nClassifying Data, p. 342<br \/>\nWriting Exponential Functions, p. 343<br \/>\nUsing Exponential and Logarithmic Regression, p. 345<\/p>\n<p><strong>Mathematical Practices<\/strong><br \/>\nQuestion 1.<br \/>\nExplain how you used properties of logarithms to rewrite the function in part (b) of Exercise 45 on page 332.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nHow can you use cases to analyze the argument given in Exercise 46 on page 339?<br \/>\nAnswer:<\/p>\n<p><strong>Performance Task Measuring Natural Disasters<\/strong><br \/>\nIn 2005, an earthquake measuring 4.1 on the Richter scale barely shook the city of Ocotillo, California, leaving virtually no damage. But in 1906, an earthquake with an estimated 8.2 on the same scale devastated the city of San Francisco. Does twice the measurement on the Richter scale mean twice the intensity of the earthquake?<br \/>\nTo explore the answers to these questions and more, go to BigIdeasMath.com.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40355\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions 6.7 31\" width=\"357\" height=\"374\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-31.png 357w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions-6.7-31-286x300.png 286w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><\/p>\n<h3><a id=\"Exponential_and_Logarithmic_Functions_Chapter_Review\"><\/a>Exponential and Logarithmic Functions Chapter Review<\/h3>\n<p><strong>6.1 Exponential Growth and Decay Functions (pp. 295\u2013302)<\/strong><\/p>\n<p>Tell whether the function represents exponential growth or exponential decay. Identify the percent increase or decrease. Then graph the function.<br \/>\nQuestion 1.<br \/>\nf (x) = (\\(\\frac{1}{3}\\))<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ny = 5<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nf(x) = (0.2)<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nYou deposit $1500 in an account that pays 7% annual interest. Find the balance after 2 years when the interest is compounded daily.<br \/>\nAnswer:<\/p>\n<p><strong>6.2 The Natural Base e (pp. 303\u2013308)<\/strong><\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 5.<br \/>\ne<sup>4<\/sup> \u2022 e<sup>11<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{20 e^{3}}{10 e^{6}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n(\u22123e<sup>-5x<\/sup>)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Tell whether the function represents exponential growth or exponential decay. Then graph the function.<br \/>\nQuestion 8.<br \/>\nf(x) = \\(\\frac{1}{3}\\)e<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ny = 6e<sup>-x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\ny = 3e<sup>-0.75x<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>6.3 Logarithms and Logarithmic Functions (pp. 309\u2013316)<\/strong><\/p>\n<p><strong>Evaluate the logarithm.<\/strong><br \/>\nQuestion 11.<br \/>\nlog<sub>2<\/sub> 8<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nlog<sub>6<\/sub> \\(\\frac{1}{36}\\)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nlog<sub>2<\/sub> 1<br \/>\nAnswer:<\/p>\n<p>Find the inverse of the function.<br \/>\nQuestion 14.<br \/>\nf(x) = 8<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\ny = ln(x \u2212 4)<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\ny = log(x+ 9)<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nGraph y = log<sub>1\/5<\/sub> x.<br \/>\nAnswer:<\/p>\n<p><strong>6.4 Transformations of Exponential and Logarithmic Functions (pp. 317\u2013324)<\/strong><\/p>\n<p><strong>Describe the transformation of f represented by g. Then graph each function.<\/strong><br \/>\nQuestion 18.<br \/>\nf(x) = e<sup>-x<\/sup>, g(x) = <sup>-5x<\/sup> \u2212 8<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nf(x) = log<sub>4<\/sub> x, g(x) = \\(\\frac{1}{2}\\)log<sub>4<\/sub> (x + 5)<br \/>\nAnswer:<\/p>\n<p>Write a rule for g.<br \/>\nQuestion 20.<br \/>\nLet the graph of g be a vertical stretch by a factor of 3, followed by a translation 6 units left and 3 units up of the graph of f(x) = e<sup>x<\/sup>.<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\nLet the graph of g be a translation 2 units down, followed by a reflection in the y-axis of the graph of f(x) = log x.<br \/>\nAnswer:<\/p>\n<p><strong>6.5 Properties of Logarithms (pp. 327\u2013332)<\/strong><\/p>\n<p><strong>Expand or condense the logarithmic expression.<\/strong><br \/>\nQuestion 22.<br \/>\nlog<sub>8<\/sub> 3xy<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nlog 10x<sup>3<\/sup>y<br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\nln \\(\\frac{3 y}{x^{5}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n3 log<sub>7<\/sub> 4 + log<sub>7<\/sub> 6<br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\nlog<sub>2<\/sub> 12 \u2212 2 log<sub>2<\/sub> x<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n2 ln x + 5 ln 2 \u2212 ln 8<br \/>\nAnswer:<\/p>\n<p>Use the change-of-base formula to evaluate the logarithm.<br \/>\nQuestion 28.<br \/>\nlog<sub>2<\/sub> 10<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nlog<sub>7<\/sub> 9<br \/>\nAnswer:<\/p>\n<p>Question 30.<br \/>\nlog<sub>23<\/sub> 42<br \/>\nAnswer:<\/p>\n<p><strong>6.6 Solving Exponential and Logarithmic Equations (pp. 333\u2013340)<\/strong><\/p>\n<p><strong>Solve the equation. Check for extraneous solutions.<\/strong><br \/>\nQuestion 31.<br \/>\n5<sup>x<\/sup> = 8<br \/>\nAnswer:<\/p>\n<p>Question 32.<br \/>\nlog<sub>3<\/sub> (2x \u2212 5) = 2<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\nln x + ln(x + 2) = 3<br \/>\nAnswer:<\/p>\n<p>Solve the inequality.<br \/>\nQuestion 34.<br \/>\n6<sup>x<\/sup> &gt; 12<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\nln x \u2264 9<br \/>\nAnswer:<\/p>\n<p>Question 36.<br \/>\ne<sub>4x-2<\/sub> \u2265 16<br \/>\nAnswer:<\/p>\n<p><strong>6.7 Modeling with Exponential and Logarithmic Functions (pp. 341\u2013348)<\/strong><\/p>\n<p><strong>Write an exponential model for the data pairs (x, y).<\/strong><br \/>\nQuestion 37.<br \/>\n(3, 8), (5, 2)<br \/>\nAnswer:<\/p>\n<p>Question 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-cr-38.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions cr 38\" width=\"258\" height=\"61\" \/><br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\nA shoe store sells a new type of basketball shoe. The table shows the pairs sold s over time t (in weeks). Use a graphing calculator to find a logarithmic model of the form s = a +b ln t that represents the data. Estimate how many pairs of shoes are sold after 6 weeks.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40357\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-cr-39.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions cr 39\" width=\"253\" height=\"68\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Exponential_and_Logarithmic_Functions_Chapter_Test\"><\/a>Exponential and Logarithmic Functions Chapter Test<\/h3>\n<p><strong>Graph the equation. State the domain, range, and asymptote.<\/strong><br \/>\nQuestion 1.<br \/>\ny = (\\(\\frac{1}{2}\\))<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ny = log<sub>1\/5<\/sub> x<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\ny = 4e<sup>-2x<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>Describe the transformation of f represented by g. Then write a rule for g.<\/strong><br \/>\nQuestion 4.<br \/>\nf(x) = log x<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-ct-4.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions ct 4\" width=\"178\" height=\"135\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nf(x) = e<sup>x<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-ct-5.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions ct 5\" width=\"161\" height=\"139\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nf(x) = \\(\\frac{1}{4}\\))<sup>x<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-ct-6.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions ct 6\" width=\"162\" height=\"135\" \/><br \/>\nAnswer:<\/p>\n<p>Evaluate the logarithm. Use log<sub>3<\/sub> 4 \u2248 1.262 and log<sub>3<\/sub> 13 \u2248 2.335, if necessary.<br \/>\nQuestion 7.<br \/>\nlog<sub>2<\/sub> 52<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nlog<sub>3<\/sub> \\(\\frac{13}{9}\\)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nlog<sub>3<\/sub> 16<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nlog<sub>3<\/sub> 8 + log<sub>3<\/sub> \\(\\frac{1}{2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nDescribe the similarities and differences in solving the equations 4<sup>5x-2<\/sup> = 16 and log<sub>4<\/sub>(10x + 6) = 1. Then solve each equation.<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nWithout calculating, determine whether log<sub>5<\/sub>11, \\(\\frac{\\log 11}{\\log 5}\\), and \\(\\frac{\\ln 11}{\\ln 5}\\) are equivalent expressions. Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nThe amount y of oil collected by a petroleum company drilling on the U.S. continental shelf can be modeled by y = 12.263 ln x \u2212 45.381, where y is measured in billions of barrels and x is the number of wells drilled. About how many barrels of oil would you expect to collect after drilling 1000 wells? Find the inverse function and describe the information you obtain from finding the inverse.<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nThe percent L of surface light that filters down through bodies of water can be modeled by the exponential function L(x) = 100e<sup>kx<\/sup>, where k is a measure of the murkiness of the water and x is the depth (in meters) below the surface.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40361\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-ct-14.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions ct 14\" width=\"145\" height=\"255\" \/><br \/>\na. A recreational submersible is traveling in clear water with a k-value of about \u22120.02. Write a function that gives the percent of surface light that filters down through clear water as a function of depth.<br \/>\nb. Tell whether your function in part (a) represents exponential growth or exponential decay. Explain your reasoning.<br \/>\nc. Estimate the percent of surface light available at a depth of 40 meters.<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nThe table shows the values y (in dollars) of a new snowmobile after x years of ownership. Describe three different ways to find an exponential model that represents the data. Then write and use a model to find the year when the snowmobile is worth $2500.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-ct-15.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 6 Exponential and Logarithmic Functions ct 15\" width=\"448\" height=\"73\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-ct-15.png 448w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-6-Exponential-and-Logarithmic-Functions-ct-15-300x49.png 300w\" sizes=\"(max-width: 448px) 100vw, 448px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Exponential_and_Logarithmic_Functions_Cumulative_Assessment\"><\/a>Exponential and Logarithmic Functions Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nSelect every value of b for the equation y = b<sup>x<\/sup> that could result in the graph shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-ca-1.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions ca 1\" width=\"359\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-ca-1.png 359w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-ca-1-300x141.png 300w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nYour friend claims more interest is earned when an account pays interest compounded continuously than when it pays interest compounded daily. Do you agree with your friend? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nYou are designing a rectangular picnic cooler with a length four times its width and height twice its width. The cooler has insulation that is 1 inch thick on each of the four sides and 2 inches thick on the top and bottom.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-ca-3.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions ca 3\" width=\"221\" height=\"154\" \/><br \/>\na. Let x represent the width of the cooler. Write a polynomial function T that gives the volume of the rectangular prism formed by the outer surfaces of the cooler.<br \/>\nb.Write a polynomial function C for the volume of the inside of the cooler.<br \/>\nc. Let I be a polynomial function that represents the volume of the insulation. How is I related to T and C?<br \/>\nd. Write I in standard form. What is the volume of the insulation when the width of the cooler is 8 inches?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nWhat is the solution to the logarithmic inequality \u22124 log<sub>2<\/sub> x \u2265 \u221220?<br \/>\nA. x \u2264 32<br \/>\nB. 0 \u2264 x \u2264 32<br \/>\nC. 0 &lt; x \u2264 32<br \/>\nD. x \u2265 32<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nDescribe the transformation of f(x) = log<sub>2<\/sub> x represented by the graph of g.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-ca-5.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions ca 5\" width=\"253\" height=\"165\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nLet f(x) = 2x<sup>3<\/sup> \u2212 4x<sup>2<\/sup> + 8x\u2212 1, g(x) = 2x \u2212 3x<sup>4<\/sup> \u2212 6x<sup>3<\/sup>+ 5, and h(x) = \u22127 + x<sup>2<\/sup> + x. Order the following functions from least degree to greatest degree.<br \/>\nA. (f + g)(x)<br \/>\nB. (hg)(x)<br \/>\nC. (h \u2212 f)(x)<br \/>\nD. (fh)(x)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nWrite an exponential model that represents each data set. Compare the two models.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40366\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-ca-7.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions ca 7\" width=\"542\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-ca-7.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-ca-7-300x106.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nChoose a method to solve each quadratic equation. Explain your choice of method.<br \/>\na. x<sup>2<\/sup> + 4x = 10<br \/>\nb. x<sup>2<\/sup> = \u221212<br \/>\nc. 4(x \u2212 1)<sup>2<\/sup> = 6x + 2<br \/>\nd. x<sup>x<\/sup> \u2212 3x \u2212 18 = 0<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nAt the annual pumpkin-tossing contest, contestants compete to see whose catapult will send pumpkins the longest distance. The table shows the horizontal distances y (in feet) a pumpkin travels when launched at different angles x (in degrees). Create a scatter plot of the data. Do the data show a linear, quadratic, or exponential relationship? Use technology to find a model for the data. Find the angle(s) at which a launched pumpkin travels 500 feet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40367\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-ca-9.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 6 Exponential and Logarithmic Functions ca 9\" width=\"398\" height=\"80\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-ca-9.png 398w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-6-Exponential-and-Logarithmic-Functions-ca-9-300x60.png 300w\" sizes=\"(max-width: 398px) 100vw, 398px\" \/><br \/>\nAnswer:<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Want to master in Algebra 2 Ch 6 Concepts like Exponential Growth and Decay Functions, Natural Base e, Logarithms, and its functions, properties of logarithms, etc.? Then, accessing this guide is the perfect solution for your concerns. Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions make you understand the topics quickly &#8230; <a title=\"Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-2-answers-chapter-6\/\" aria-label=\"More on Big Ideas Math Algebra 2 Answers Chapter 6 Exponential and Logarithmic Functions\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":89291,"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-2-Answers-Chapter-6-Exponential-and-Logarithmic-Functions.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/40223"}],"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=40223"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/40223\/revisions"}],"predecessor-version":[{"id":90329,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/40223\/revisions\/90329"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89291"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=40223"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=40223"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=40223"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}