Chapter 5: Inverse, Exponential, and Logarithmic Functions

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Presentation transcript:

Chapter 5: Inverse, Exponential, and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions 5.3 Logarithms and Their Properties 5.4 Logarithmic Functions 5.5 Exponential and Logarithmic Equations and Inequalities 5.6 Further Applications and Modeling with Exponential and Logarithmic Functions

Exponential Functions If b > 0, b  1, then f (x) = bx defines the exponential function with base, b. b is the growth or decay factor. Note: The transformation (translations) rules also apply to exponential functions. f(x) = a  b(x-h) +k , where a, h and k tell us how the functions moves

Graphs of Exponential Functions Example Graph f(x) = 2x. Determine the domain and range of f.

Graphs of Exponential Functions (Growth) Example Graph f(x) = 2x. Determine the domain and range of f.

Graphs of Exponential Functions (Decay) Example Graph f(x) = ½ x. Determine the domain and range of f.

Using Translations to Graph an Exponential Function

Exponential Equations (Type I)

Exponential Equations (Type I)

Compound Interest Formula Suppose that a principal of P dollars is invested at an annual interest rate r (in decimal form), compounded n times per year. Then, the amount A accumulated after t years is given by the formula

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The Natural Number e e is an irrational number Since e is an important base, calculators are programmed to find powers of e.

Continuous Compounding Formula If an amount of P dollars is deposited at a rate of interest r (in decimal form) compounded continuously for t years, then the final amount in dollars is A = Pert. Example Suppose $5000 is deposited in an account paying 3% compounded continuously for 5 years. Find the total amount on deposit at the end of 5 years.

Continuous Compounding Formula If an amount of P dollars is deposited at a rate of interest r (in decimal form) compounded continuously for t years, then the final amount in dollars is A = Pert. Example Suppose $5000 is deposited in an account paying 3% compounded continuously for 5 years. Find the total amount on deposit at the end of 5 years. Solution A = 5000e0.03(5) = 5000e0.15 ≈ 5809.17 The final balance is $5809.17.