1. 8.5 and 8.6 Writing and Graphing Exponential Growth and Decay Functions Students will learn to Write exponential growth and decay functions Graph exponential growth and decay functions Identify domain, range, y-intercepts and asymptotes

2. Recall the rate of change of linear functions. x-2012 y-5-313 +1 +1 +1+1 +2 +2+2 +2 A linear function has a constant rate of change.

3. How is this data changing? x-2012 y2618 +1 +1 +1+1 The rate of change is not constant.

4. How is this data changing? x-2012 y2618 +1 +1 +1+1 This is called exponential growth.

5. Let’s find a rule! xyy -2 02 16 218 xy

6. Write a rule for each function. x-2012 y 141664256 x-2012 y The values in these functions are increasing. They are exponential growth functions.

7. What is happening now? x-2012 y1263 This is an exponential decay function.

8. Identify as exponential growth, decay, or neither. Write a rule if possible. x-2012 y124816 x-2012 y10836124 x-2012 y2412632

9. Summary a is the initial amount r is the growth (or decay) rate if r > 1 ------- growth if 0 < r < 1 – decay (1+r) is the growth(or decay) factor t is the time period

10. Is this exponential growth or decay? Initial amount: Growth (or decay) rate: Growth (or decay) factor:

11. Now, to graph an exponential function. xy -2 02 16 218 Domain: {all real numbers} Range: {y > 0} Asymptote: y = 0 Y-intercept: (0, 2)

12. Graph the exponential function. xy -2 0 1 2 Domain: Range: Asymptote: Y-intercept:

13. Graph the exponential function. xy -2 0 1 2 Domain: Range: Asymptote: Y-intercept:

14. Summary Domain: {all real numbers} Range: {y > 0} if a >0 and {y < 0} if a < 0 Asymptote: y = 0 Y-intercept: (0, a)

15. xy -2 0 1 2

17. Observations?

18. Homework Page 523 #2-5, 9, 13, 17, 22, 26, 30, 34 Page 535 #2, 4, 6, 9, 18, 19, 20, 24, 28, 38-41