1. Copyright © 2009 Pearson Education, Inc. Slide 5 - 1 Active Learning Lecture Slides For use with Classroom Response Systems © 2009 Pearson Education, Inc. Chapter 5 Exponential and Logarithmic Functions

2. Copyright © 2009 Pearson Education, Inc. Slide 5 - 2 CHAPTER 5: Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions and Graphs 5.3 Logarithmic Functions and Graphs 5.4 Properties of Logarithmic Functions 5.5 Solving Exponential and Logarithmic Equations 5.6 Applications and Models: Growth and Decay; and Compound Interest

3. Copyright © 2009 Pearson Education, Inc. Slide 5 - 3 Find the inverse of the relation a. c. b. d.

4. Copyright © 2009 Pearson Education, Inc. Slide 5 - 4 Find the inverse of the relation a. c. b. d.

5. Copyright © 2009 Pearson Education, Inc. Slide 5 - 5 Find the inverse of the relation a. c. b. d.

6. Copyright © 2009 Pearson Education, Inc. Slide 5 - 6 Find the inverse of the relation a. c. b. d.

7. Copyright © 2009 Pearson Education, Inc. Slide 5 - 7 Find a formula for the inverse of the function f(x) = 10 – 6x. a. c. b. d.

8. Copyright © 2009 Pearson Education, Inc. Slide 5 - 8 Find a formula for the inverse of the function f(x) = 10 – 6x. a. c. b. d.

9. Copyright © 2009 Pearson Education, Inc. Slide 5 - 9 Find a formula for the inverse of the function f(x) = 2x+5. a. c. b. d.

10. Copyright © 2009 Pearson Education, Inc. Slide 5 - 10 Find a formula for the inverse of the function f(x) = 2x+5. a. c. b. d.

11. Copyright © 2009 Pearson Education, Inc. Slide 5 - 11 Which of the following functions is one-to-one? a.b. c.d.

12. Copyright © 2009 Pearson Education, Inc. Slide 5 - 12 Which of the following functions is one-to-one? a.b. c.d.

13. Copyright © 2009 Pearson Education, Inc. Slide 5 - 13 Which of the following graphs illustrates the graph of f(x) = 4 x. a.b. c.d.

14. Copyright © 2009 Pearson Education, Inc. Slide 5 - 14 Which of the following graphs illustrates the graph of f(x) = 4 x. a.b. c.d.

15. Copyright © 2009 Pearson Education, Inc. Slide 5 - 15 Which of the following graphs illustrates the graph of f(x) = –2 x – 1. a.b. c.d.

16. Copyright © 2009 Pearson Education, Inc. Slide 5 - 16 Which of the following graphs illustrates the graph of f(x) = –2 x – 1. a.b. c.d.

17. Copyright © 2009 Pearson Education, Inc. Slide 5 - 17 Find the approximate value of e  0.16 to four decimal places. a. –1.1735 c. 0.8521 b. –0.8521 d. 1.0161

18. Copyright © 2009 Pearson Education, Inc. Slide 5 - 18 Find the approximate value of e –0.16 to four decimal places. a. –1.1735 c. 0.8521 b. –0.8521 d. 1.0161

19. Copyright © 2009 Pearson Education, Inc. Slide 5 - 19 Using the compound interest formula, determine the approximate amount in the account after 5 years if the investment is $1500 at an interest rate of 8.2% compounded quarterly. a. $2195.64 c. $2260.23 b. $2250.88 d. $2271.56

20. Copyright © 2009 Pearson Education, Inc. Slide 5 - 20 Using the compound interest formula, determine the approximate amount in the account after 5 years if the investment is $1500 at an interest rate of 8.2% compounded quarterly. a. $2195.64 c. $2260.23 b. $2250.88 d. $2271.56

21. Copyright © 2009 Pearson Education, Inc. Slide 5 - 21 Suppose a school deposited a $1000 scholarship in an account paying 7.9% interest compounded quarterly. Approximately how much will the scholarship be worth in two years? a. $1169.36 c. $1268.77 b. $1250.98 d. $1316.42

22. Copyright © 2009 Pearson Education, Inc. Slide 5 - 22 Suppose a school deposited a $1000 scholarship in an account paying 7.9% interest compounded quarterly. Approximately how much will the scholarship be worth in two years? a. $1169.36 c. $1268.77 b. $1250.98 d. $1316.42

23. Copyright © 2009 Pearson Education, Inc. Slide 5 - 23 Convert to a logarithmic equation: 2 x = 20. a. x = log 2 20 c. 2 = log x 20 b. x = log10 d. x = log 20 2

24. Copyright © 2009 Pearson Education, Inc. Slide 5 - 24 Convert to a logarithmic equation: 2 x = 20. a. x = log 2 20 c. 2 = log x 20 b. x = log10 d. x = log 20 2

25. Copyright © 2009 Pearson Education, Inc. Slide 5 - 25 Convert to an exponential equation: log 3 x = 5. a. x = 5 3 c. x 5 = 3 b. x = 3 5 d. x 3 = 5

26. Copyright © 2009 Pearson Education, Inc. Slide 5 - 26 Convert to an exponential equation: log 3 x = 5. a. x = 5 3 c. x 5 = 3 b. x = 3 5 d. x 3 = 5

27. Copyright © 2009 Pearson Education, Inc. Slide 5 - 27 Find ln 3 using a calculator. Round to four decimal places. a. 0.4771 c. 20.0855 b. 1.0986 d. 1000

28. Copyright © 2009 Pearson Education, Inc. Slide 5 - 28 Find ln 3 using a calculator. Round to four decimal places. a. 0.4771 c. 20.0855 b. 1.0986 d. 1000

29. Copyright © 2009 Pearson Education, Inc. Slide 5 - 29 Find log 0.001. Do not use a calculator. a. –4 c. 3 b. –3 d. 1000

30. Copyright © 2009 Pearson Education, Inc. Slide 5 - 30 Find log 0.001. Do not use a calculator. a. –4 c. 3 b. –3 d. 1000

31. Copyright © 2009 Pearson Education, Inc. Slide 5 - 31 Find log 5 8 using the change-of-base formula. a. 0.2041 c. 1.2920 b. 0.7740 d. 1.6

32. Copyright © 2009 Pearson Education, Inc. Slide 5 - 32 Find log 5 8 using the change-of-base formula. a. 0.2041 c. 1.2920 b. 0.7740 d. 1.6

33. Copyright © 2009 Pearson Education, Inc. Slide 5 - 33 Express in terms of sums and differences of logarithms: a. c. b. d.

34. Copyright © 2009 Pearson Education, Inc. Slide 5 - 34 Express in terms of sums and differences of logarithms: a. c. b. d.

35. Copyright © 2009 Pearson Education, Inc. Slide 5 - 35 Express in terms of sums and differences of logarithms: a. c. b. d.

36. Copyright © 2009 Pearson Education, Inc. Slide 5 - 36 Express in terms of sums and differences of logarithms: a. c. b. d.

37. Copyright © 2009 Pearson Education, Inc. Slide 5 - 37 Given that log c 2 = 0.3333 and log c 12 = 1.1950, find log c 6. a. 3.5854 c. 0.8617 b. 0.9999 d. 0.1951

38. Copyright © 2009 Pearson Education, Inc. Slide 5 - 38 Given that log c 2 = 0.3333 and log c 12 = 1.1950, find log c 6. a. 3.5854 c. 0.8617 b. 0.9999 d. 0.1951

39. Copyright © 2009 Pearson Education, Inc. Slide 5 - 39 Given that log a 3 = 0.6826 and log a 4 = 0.8614, find log a 36. a. 0.4014 c. 2.2266 b. 1.1760 d. 4.6320

40. Copyright © 2009 Pearson Education, Inc. Slide 5 - 40 Given that log a 3 = 0.6826 and log a 4 = 0.8614, find log a 36. a. 0.4014 c. 2.2266 b. 1.1760 d. 4.6320

41. Copyright © 2009 Pearson Education, Inc. Slide 5 - 41 Simplify: lne 6t. a. e -6t c. 6t b. te 6 d. –6t

42. Copyright © 2009 Pearson Education, Inc. Slide 5 - 42 Simplify: lne 6t. a. e -6t c. 6t b. te 6 d. –6t

43. Copyright © 2009 Pearson Education, Inc. Slide 5 - 43 Solve: log 3 (3x + 6) – log 3 (x – 6) = 2. a. 14 c. b. 10 d. Does not exist

44. Copyright © 2009 Pearson Education, Inc. Slide 5 - 44 Solve: log 3 (3x + 6) – log 3 (x – 6) = 2. a. 14 c. b. 10 d. Does not exist

45. Copyright © 2009 Pearson Education, Inc. Slide 5 - 45 Solve: log 2 (x + 5) + log 2 (x – 1) = 4. a. c. 5 b. 3 d. 6

46. Copyright © 2009 Pearson Education, Inc. Slide 5 - 46 Solve: log 2 (x + 5) + log 2 (x – 1) = 4. a. c. 5 b. 3 d. 6

47. Copyright © 2009 Pearson Education, Inc. Slide 5 - 47 Solve: log 2 (x – 3) + log 2 (2x – 10) = 4. a. 4 c. b. 7 d. No solution

48. Copyright © 2009 Pearson Education, Inc. Slide 5 - 48 Solve: log 2 (x – 3) + log 2 (2x – 10) = 4. a. 4 c. b. 7 d. No solution

49. Copyright © 2009 Pearson Education, Inc. Slide 5 - 49 Solve: 2 5+x = 32 x-4. a. c. b. d.

50. Copyright © 2009 Pearson Education, Inc. Slide 5 - 50 Solve: 2 5+x = 32 x-4. a. c. b. d.

51. Copyright © 2009 Pearson Education, Inc. Slide 5 - 51 Solve: 3 5+4x = 9 x. a. c. b. –5 d.

52. Copyright © 2009 Pearson Education, Inc. Slide 5 - 52 Solve: 3 5+4x = 9 x. a. c. b. –5 d.

53. Copyright © 2009 Pearson Education, Inc. Slide 5 - 53 The population of a city doubled in 12 years. What was the approximate exponential growth rate? a. 16.7% c. 5.8% b. 6.0% d. 2.48%

54. Copyright © 2009 Pearson Education, Inc. Slide 5 - 54 The population of a city doubled in 12 years. What was the approximate exponential growth rate? a. 16.7% c. 5.8% b. 6.0% d. 2.48%

55. Copyright © 2009 Pearson Education, Inc. Slide 5 - 55 The population of a city doubled in 10 years. What was the approximate exponential growth rate? a. 3.0% c. 6.9% b. 5.0% d. 14.4%

56. Copyright © 2009 Pearson Education, Inc. Slide 5 - 56 The population of a city doubled in 10 years. What was the approximate exponential growth rate? a. 3.0% c. 6.9% b. 5.0% d. 14.4%

57. Copyright © 2009 Pearson Education, Inc. Slide 5 - 57 Suppose $2000 is invested at interest rate, k, compounded continuously, and grows to $2,473.53 in 5 years. Find the approximate interest rate. a. 3.83% c. 4.75% b. 4.25% d. 7.89%

58. Copyright © 2009 Pearson Education, Inc. Slide 5 - 58 Suppose $2000 is invested at interest rate, k, compounded continuously, and grows to $2.473.53 in 5 years. Find the approximate interest rate. a. 3.83% c. 4.75% b. 4.25% d. 7.89%

59. Copyright © 2009 Pearson Education, Inc. Slide 5 - 59 Suppose $2000 is invested at interest rate, k, compounded continuously, and grows to $2.473.53 in 5 years. Find the approximate doubling time. a. 7.1 years c. 16.3 years b. 14.6 years d. 21.1 years

60. Copyright © 2009 Pearson Education, Inc. Slide 5 - 60 Suppose $2000 is invested at interest rate, k, compounded continuously, and grows to $2.473.53 in 5 years. Find the approximate doubling time. a. 7.1 years c. 16.3 years b. 14.6 years d. 21.1 years

61. Copyright © 2009 Pearson Education, Inc. Slide 5 - 61 Suppose $8000 is invested at interest rate, k, compounded continuously, and grows to $10,962.07 in 5 years. Approximate the amount in the account after 10 years. a. $13,924.14 c. $15,020.87 b. $14,259.22 d. $15,664.41

62. Copyright © 2009 Pearson Education, Inc. Slide 5 - 62 Suppose $8000 is invested at interest rate, k, compounded continuously, and grows to $10,962.07 in 5 years. Approximate the amount in the account after 10 years. a. $13,924.14 c. $15,020.87 b. $14,259.22 d. $15,664.41