How do I graph and use exponential growth and decay functions?

4.5 Graph Exponential Decay Functions Exponential Functions Functions of the form: Exponential growth if b > 1, where b is the growth factor. Exponential decay if b < 1, where b is the decay factor.

4.5 Graph Exponential Decay Functions Example 1 Graph y = b x for 0 < b < 1 Graph y = (½) x. Analyze the graph. Find the average rate of change over the interval  2 < x < 2. Step 1 Make a table of values. x y Step 2 Plot the points from the table. Step 3 Draw from right to left, a smooth curve that begins just ______ the x-axis, passes through the plotted points, and moves _________________. above up to the left

4.5 Graph Exponential Decay Functions Example 1 Graph y = b x for 0 < b < 1 Graph y = (½) x. Analyze the graph. Find the average rate of change over the interval  2 < x < 2. Step 4 Examine the graph. The y-intercept of the function is __. As the value of x approaches the value of the function approaches _____. 1 As the value of x approaches, the value of the function approaches ___. Also the function is decreasing on the interval __________. Using the points (-2, 4), and (2, ¼ ), the average rate of change over the interval -2 < x < 2 is _______, or about ______. 0

4.5 Graph Exponential Decay Functions Checkpoint. Complete the following exercises. 1.Graph y = ( ¼ ) x and find the average rate of change over the interval  2 < x < 2. x y

4.5 Graph Exponential Decay Functions Example 2 Graph y = ab x for 0 < b < 1 Then, from right to left, draw a curve that begins just ______ the x-axis, passes through the two points, and moves _______ to the left. below down Solution Plot and

4.5 Graph Exponential Decay Functions Checkpoint. Complete the following exercises. 2.Graph the function. State the domain and range. Translation: left 1 unit down 3 units Domain: All real numbers Range: Asymptote:

4.5 Graph Exponential Decay Functions Example 4 Find a value after depreciation The initial amount is a = ______ and the percent of decrease is r = ______. So the model is: Solution Televisions A new television costs $1200. The value of the television decreases by 21% each year. Write an exponential decay model giving the television’s value y (in dollars) after t years. Estimate the value after 2 years. Write exponential decay formula. Substitute for a and r. Simplify. When t = 2, the television’s value is y = 1200 ( 0.79 ) 2 = ________.

4.5 Graph Exponential Decay Functions Checkpoint. Complete the following exercises. 3.Rework Example 4, with a 12% decrease each year.

4.5 Graph Exponential Decay Functions Pg. 139, 4.5 #1-17