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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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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.
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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.
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1-4 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-5 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-6 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-7 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-8 Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-10 EXAMPLE 3 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-14 EXAMPLE 5 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-17 EXAMPLE 7 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-19 EXAMPLE 8 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-20 EXAMPLE X CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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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.
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1-32 EXAMPLE 7 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-33 EXAMPLE 7 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-35 EXAMPLE 8 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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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.
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1-47 EXAMPLE 7 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-51 EXAMPLE 8C CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-54 EXAMPLE 10 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-55 EXAMPLE 10 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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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.
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1-66 EXAMPLE 7 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-73 EXAMPLE 11 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-78 EXAMPLE 14 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-81 EXAMPLE 15 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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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.
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1-89 EXAMPLE 3 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-96 EXAMPLE 7 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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1-99 EXAMPLE 8 CONTINUED Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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