The function is ,, where is the number of years since .

The values in the graph corresponding years.

**(a)** Graph the equation.

, .

**(b)** Find the average rate of change from to .

Observe the graph:

Average rate of change of on the interval .

Average rate of change from to was about .

This value represents the average change in net personal income in the U.S. from to .

**(c) **Find the period was the average rate of change highest:

The highest average rate of change will occur at the steepest point of the graph.

Locate the steepest points on the graph.

Average rate of change of on the interval .

This value represents the average change in net personal income in the U.S. from to .

Average rate of change from to was about .

Find the period was the average rate of change lowest:

the lowest average rate of change will occur at the flattest point of the graph.

Locate the steepest points on the graph.

Average rate of change of on the interval .

This value represents the average change in net personal income in the U.S. from to .

Average rate of change from to was about .

**(a)** Graph of the equation.

, .

**(b)** Average rate of change from to was about .

This value represents the average change in net personal income in the U.S. from to .

**(c)** The rate of change was highest from to at about and lowest from to at about .

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