1. Objectives: The student will be able to… 1)Graph exponential functions. 2)Solve exponential equations and inequalities.

3. Example 1 xy

4. Exponential Functions Take the form y = ab x Base (b) is a constant Exponent is a variable Example: a = b = The x-axis is an asymptote of the general graph. The graph contains the point (0, a).

5. Two Types of Exponential Functions Exponential Growth - Base is a number greater than 1 Exponential Decay -base is a number between 0 and 1

6. Sketch a graph of the exponential function. Then state the domain and range. Indicate if it is a growth or decay.

7. Example 2 Determine whether each function represents exponential growth or decay. a) b) c)

8. Word Problems! Text p. 528

9. Text p. 529

10. Text p. 525

12. Homework Text p. 528 #s 19-32 all #s 59-61

13. Exponential Equations and Inequalities Since the domain of an exponential function includes irrational numbers such as, all the properties of rational exponents apply to irrational exponents. Example 4: Simplify each expression:

14. Simplify each exponential expression:

15. Property of Equality for Exponential Functions If b is a positive number other than 1, then b x = b y if and only if x = y. Example: If 2 x = 2 8, then x = 8

16. Example 5: Solve each equation

17. Example 6: Solve the inequality

18. Solve each exponential equation or inequality.

19. Homework Text p. 528 #s 39-55 odd #s 57-58