1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Exponential Growth and Decay Section 6.4

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 2 What you’ll learn about Separable Differential Equations Law of Exponential Change Continuously Compounded Interest Modeling Growth with Other Bases Newton’s Law of Cooling … and why Understanding the differential equation gives us new insight into exponential growth and decay.

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 3 Separable Differential Equation

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 4 Example Solving by Separation of Variables

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 5 The Law of Exponential Change

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 6 Continuously Compounded Interest

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 7 Example Compounding Interest Continuously

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 8 Example Finding Half-Life

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 9 Half-life

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 10 Newton’s Law of Cooling

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 6- 11 Example Using Newton’s Law of Cooling A temperature probe is removed from a cup of coffee and placed in water that has a temperature of T = 4.5 C. Temperature readings T, as recorded in the table below, are taken after 2 sec, 5 sec, and every 5 sec thereafter. Estimate (a)the coffee's temperature at the time the temperature probe was removed. (b)the time when the temperature probe reading will be 8 C. o S o

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Pages 338-339 (15, 19, 25, 27, 29) Slide 6- 12