1. 1 Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 3.1 Exponential Functions Demana, Waits, Foley, Kennedy

2. 2 Copyright © 2015, 2011, and 2007 Pearson Education, Inc. What you’ll learn about Exponential Functions and Their Graphs Population Models Radioactive Decay … and why Exponential functions model many growth patterns, including the growth of human and animal populations.

3. 3 Copyright © 2015, 2011, and 2007 Pearson Education, Inc. Finding the value of b with a calculator A) B) C)

4. 4 Copyright © 2015, 2011, and 2007 Pearson Education, Inc. Compute the exact value for the given x without a calculator A) for x = 0 B) for x = -3

5. 5 Copyright © 2015, 2011, and 2007 Pearson Education, Inc. Exponential Functions

6. 6 Copyright © 2015, 2011, and 2007 Pearson Education, Inc. Example Finding an Exponential Function from its Table of Values

7. 7 Copyright © 2015, 2011, and 2007 Pearson Education, Inc. Example Finding an Exponential Function from its Table of Values

8. 8 Copyright © 2015, 2011, and 2007 Pearson Education, Inc. Population of Two Major Cities City Population Population in 1950 in 1968 Houston 596,163 913,617 San Antonio 500,460 677,870 What year will San Antonio have 900,000 people? When will the two Cities have the same population?

9. 9 Copyright © 2015, 2011, and 2007 Pearson Education, Inc. Radioactive Decay The half-life of a certain radioactive substance is 32 days. There are 3.5grams present initially. Express a function in respect to time When will there be less than 1 grams remaining?