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Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 Chapter 4 Exponential and Logarithmic Functions.

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Presentation on theme: "Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 Chapter 4 Exponential and Logarithmic Functions."— Presentation transcript:

1 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1-1 Chapter 4 Exponential and Logarithmic Functions

2 4 Exponential and Logarithmic Functions Chapter Outline 4.1One-to-One and Inverse Functions 4.2Exponential Functions 4.3Logarithms and Logarithmic Functions 4.4Properties of Logarithms: Solving Exponential and Logarithmic Equations 4.5Applications from Business, Finance, and Science 1-2 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

3 Learning Objectives In Section 4.1 you will learn how to:  A.Identify one-to-one functions  B.Explore inverse functions using ordered pairs  C.Find inverse functions using an algebraic method  D.Graph a function and its inverse  E.Solve applications of inverse functions 4.1 One-to-One and Inverse Functions 1-3 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

4 1-4 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

5 1-5 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

6 1-6 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

7 1-7 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

8 1-8 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

9 1-9 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

10 1-10 EXAMPLE 3 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

11 1-11 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

12 1-12 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

13 1-13 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14 1-14 EXAMPLE 5 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

15 1-15 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

16 1-16 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

17 1-17 EXAMPLE 7 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

18 1-18 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

19 1-19 EXAMPLE 8 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

20 1-20 EXAMPLE X CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

21 Learning Objectives In Section 4.2 you will learn how to:  A.Evaluate an exponential function  B.Graph general exponential functions  C.Graph base-e exponential functions  D.Solve exponential equations and applications 4.2 Exponential Functions 1-21 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

22 1-22 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

23 1-23 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

24 1-24 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

25 1-25 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

26 1-26 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

27 1-27 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

28 1-28 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

29 1-29 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

30 1-30 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

31 1-31 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

32 1-32 EXAMPLE 7 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

33 1-33 EXAMPLE 7 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

34 1-34 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

35 1-35 EXAMPLE 8 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

36 1-36 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

37 Learning Objectives In Section 4.3 you will learn how to:  A.Write exponential equations in logarithmic form  B.Find common logarithms and natural logarithms  C.Graph logarithmic functions  D.Find the domain of a logarithmic function  E.Solve applications of logarithmic functions 4.3 Logarithms and Logarithmic Functions 1-37 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

38 1-38 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

39 1-39 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

40 1-40 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

41 1-41 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

42 1-42 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

43 1-43 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

44 1-44 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

45 1-45 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

46 1-46 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

47 1-47 EXAMPLE 7 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

48 1-48 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

49 1-49 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

50 1-50 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

51 1-51 EXAMPLE 8C CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

52 1-52 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

53 1-53 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

54 1-54 EXAMPLE 10 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

55 1-55 EXAMPLE 10 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

56 Learning Objectives In Section 4.4 you will learn how to:  A.Solve logarithmic equations using the fundamental properties of logarithms  B.Apply the product, quotient, and power properties of logarithms  C.Solve general logarithmic and exponential equations  D.Solve applications involving logistic, exponential, and logarithmic functions 4.4 Properties of Logarithms: Solving Exponential/Logarithmic Equations 1-56 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

57 1-57 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

58 1-58 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

59 1-59 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

60 1-60 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

61 1-61 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

62 1-62 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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64 1-64 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

65 1-65 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

66 1-66 EXAMPLE 7 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

67 1-67 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

68 1-68 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

69 1-69 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

70 1-70 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

71 1-71 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

72 1-72 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

73 1-73 EXAMPLE 11 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

74 1-74 EXAMPLE 11 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

75 1-75 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

76 1-76 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

77 1-77 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

78 1-78 EXAMPLE 14 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

79 1-79 EXAMPLE 14 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

80 1-80 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

81 1-81 EXAMPLE 15 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

82 Learning Objectives In Section 4.5 you will learn how to:  A.Calculate simple interest and compound interest  B.Calculate interest compounded continuously  C.Solve applications involving annuities and amortization  D.Solve applications of exponential growth and decay 4.5Applications from Business, Finance, and Science 1-82 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

83 1-83 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

84 1-84 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

85 1-85 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

86 1-86 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

87 1-87 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

88 1-88 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

89 1-89 EXAMPLE 3 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

90 1-90 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

91 1-91 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

92 1-92 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

93 1-93 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

94 1-94 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

95 1-95 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

96 1-96 EXAMPLE 7 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

97 1-97 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

98 1-98 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

99 1-99 EXAMPLE 8 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.


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