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

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

4.4 Graph Exponential Growth 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.

4.4 Graph Exponential Growth Functions Example 1 Graph y = b x for b > 1 Graph y = 3 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 left to right, a smooth curve that begins just ______ the x-axis, passes through the plotted points, and moves _________________. above up to the right

4.4 Graph Exponential Growth Functions Example 1 Graph y = b x for b > 1 Graph y = 3 x. Analyze the graph. Find the average rate of change over the interval  2 < x < 2. Step 4 Examine the graph. The graph intersects the y-axis at point _____. So the y-intercept of y = 3 x is __. You can see from the graph that as the value of x approaches the value (0, 1) 1 of the function approaches but never reaches ___. So the function has no zeros or x-intercepts. As the value of x approaches, the value of the function approaches _____. Also the function is increasing on the interval __________. Using the points (-2, 1/9), and (2, 9), the average rate of change over the interval -2 < x < 2 is _____, or about _____. 0

4.4 Graph Exponential Growth Functions Checkpoint. Complete the following exercises. 1.Graph y = 2 x and find the average rate of change over the interval  2 < x < 2. x y

4.4 Graph Exponential Growth Functions Example 2 Graph y = ab x for b > 1 Then, from left to right, draw a curve that begins just ______ the x-axis, passes through the two points, and moves _________________. above up to the right Solution Plot and

Then translate the graph ____________ and _____________. 4.4 Graph Exponential Growth Functions Example 3 Graph y = ab x – h + k for b > 1 State the domain and range. Solution Begin by sketching the graph of y = 2. 3 x, which passes through ( 0, ___) and ( 1, ___). 2 right 2 units down 2 units 6 The graph’s asymptote is the line _____________. The domain is all real __________, numbers and the range is __________.

4.4 Graph Exponential Growth 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:

4.4 Graph Exponential Growth Functions Pg. 134, 4.4 #1-12