Chapter 12.2, Problem 53E

To determine

To find: the prediction of the highest point the ball reaches on its 7^th bounce.

Answer to Problem 53E

0.43 feet

Explanation of Solution

Given:

  

Calculation:

General equation

  $\widehat{y}=b_0+b_{1}x$

The calculation of the constant $b_0$ is mention in the row “Constant” and in the column “Coef” of the computer output:

  $b_0=0.45374$

The calculation of the slope $b_1$ is mention in the row “Bounce” and in the column “Coef” of the computer output:

  $b_1=-0.117160$

Putting the value of $b_0$ and $b_1$

  $\begin{array}{c}\widehat{y}=b_0+b_{1}x\\ =0.45374-0.117160x\end{array}$

Where x shows the bounce number and y shows the logarithm of the height.

  $\log y=0.45374-0.117160x$

Put x by 7 and calculate:

  $\log y=0.45374-0.117160\left(7\right)=-0.36638$

Taking the exponential

  $\widehat{y}={10}^{\log y}={10}^{-0.36638}=0.43$

Therefore the expected highest point of the ball is 0.43 feet.

Hence, the correct option is (c)