Exponential and Logarithmic Functions A Look Back Until now, our study of functions has concentrated on polynomial and rational functions. These functions belong to the class of algebraic functions —that is, functions that can be expressed in terms of sums, differences, products, quotients, powers, or roots of polynomials. Functions that are not algebraic are termed transcendental . That is, they transcend, or go beyond, algebraic functions. A Look Ahead In this chapter, we study two transcendental functions: the exponential function and the logarithmic function. These functions occur frequently in a wide variety of applications, such as biology, chemistry, economics, and psychology. The chapter begins with a discussion of composite, one-to-one, and inverse functions—concepts that are needed to explain the relationship between exponential and logarithmic functions. Depreciation of Cars You are ready to buy that first new car. You know that cars lose value over time due to depreciation and that different cars have different rates of depreciation. So you will research the depreciation rates for the cars you are thinking of buying. After all, for cars that sell for about the same price, the lower the depreciation rate, the more the car will be worth each year. —See the Internet-based Chapter Project— Outline 5. 1 Composite Functions 5. 2 One-to-One Functions; Inverse Functions 5. 3 Exponential Functions 5. 4 Logarithmic Functions 5. 5 Properties of Logarithms 5. 6 Logarithmic and Exponential Equations 5. 7 Financial Models 5. 8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models 5. 9 Building Exponential, Logarithmic, and Logistic Models from Data Chapter Review Chapter Test Cumulative Review Chapter Project 5 272 Credit: Vladimir Kramin/Shutterstock
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