Chapter 7.9, Problem 4GP

To determine

To plot: the graph of the height of the tennis ball after each bounce.

Explanation of Solution

Given information:

Consider tennis ball dropped from the height $=12.\text{ feet}\text{.}$

Every time ball is bounce back to $80\%$ of the height.

Calculation:

Every time ball is bounce back to $80\%$ of the height. $20\%$ decay in the height.

Then, the height of the ball after each bounce is modeled by exponential decay function.

Decay rate is

  $\begin{array}{l}20\%\\ \Rightarrow r=0.2\end{array}$

Then the height of the ball is

  $\begin{array}{}$ y=a{(1-r)}^x$$ y=12{(1-0.2)}^x$$ y=12{(0.8)}^x$\end{array}$

Draw the graph of the function $y=12{(0.8)}^x$ .

Hence, the graph of the height of the tennis ball after each bounce is drawn.