1. Section 3-11 Bell Quiz Ch 3a 10 pts possible 2 pts

2. Section 3-12 Chapter 3 Exponential, Logistic, and Logarithmic Functions

3. Section 3-13 Ch 3 Overview Just like their algebraic cousins, exponential, logistic, and logarithmic functions have wide application. Exponential functions model growth and decay over time, such as unrestricted population growth and the decay of radioactive substances. Logistic functions model restricted population growth, certain chemical reactions, and the spread of rumors and diseases. Logarithmic functions are the basis of the Richter scale of earthquake intensity, the pH acidity scale, and the decibel measurement of sound..

4. Section 3-14 Ch 3 Overview The chapter closes with a study of the mathematics of finance, an application of exponential and logarithmic functions often used when making investments.

5. Section 3-15 3.1 Exponential and Logistic Functions

6. Section 3-16 What you’ll learn about Exponential Functions and Their Graphs The Natural Base e Population Models … and why Exponential and logistic functions model many growth patterns, including the growth of human and animal populations.

7. Section 3-17 Exponential Functions Let a and b be real number constants. An exponential function in x is a function that can be written in the form, where b is positive, and. The constant a is the initial value of f (the value at x = 0), and b is the base.

8. Section 3-18 Recognizing Exponential Functions Which of the following are exponential functions?

9. Section 3-19 Computing Exponential Function Values Find: f (4) = f (0) = f (-3) = Makes a graph (x, y) values.

10. Section 3-110 Graphing Activity Graphs of y = b x What do they have in common? Window: x-min: -5 y-min: -1 x-max: 5y-max: 5

11. Section 3-111 Generalized y = b x Domain: Range: Vertical/horizontal asymptote Intercept: Function is increasing Bounded?

12. Section 3-112 Transforming Exponential Functions Vertical Translations y = f(x) ± c: + up c units - down c units Horizontal Translations y = f(x ± c): + left c units - right c units Across the x-axis y = -f(x) Across the y-axis y = f(-x) Vertical Stretch or Shrink y = k·f(x): 0 < k < 1: V. Shrink k > 1: V. Stretch Horizontal Stretch or Shrink y = f(k·x): 0 < k < 1: H. Stretch k > 1: H. Shrink

13. Section 3-113 Example Transforming Exponential Functions Describe how to transform the graph of Right 1 Reflects across the y-axis Vertical Stretch of 3 Horizontal Shrink of 2 and reflects across the y-axis Down 1

14. Section 3-114 The Natural Base e Or e is like π e = 2.71828 F(x) = e x is the natural exponential function because of its applications in Calculus.

15. Section 3-115 Exponential Functions and the Base e

16. Section 3-116 Exponential Functions and the Base e

17. Section 3-117 Example Transforming Exponential Functions = same as other exponential functions

18. Section 3-118 Population Growth Using 20 th century U.S. census data, the population of New York state can be modeled by where P is the population in millions and t is the number of years since 1800. Based on this model, (a) What was the population of New York in 1850? (b) What will New York state’s population be in 2010? 1,794,558 19,161,673

19. Section 3-119 HOMEWORK Section 3-1 (page286) 1 - 4, 15 -17, 21 - 24, 55, 57