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

Example 1 xy

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).

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

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

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

Word Problems! Text p. 528

Text p. 529

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Homework Text p. 528 #s all #s 59-61

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:

Simplify each exponential expression:

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

Example 5: Solve each equation

Example 6: Solve the inequality

Solve each exponential equation or inequality.

Homework Text p. 528 #s odd #s 57-58