Question

Students in Mr. Handford’s class dropped a kickball beneath a motion detector. The detector recorded the height of the ball (in feet) as it bounced up and down several times. Here is a computer output from a linear regression analysis of the transformed data of log(height) versus bounce number. Predict the highest point the ball reaches on its seventh bounce.

a. $0.35$feet

b. $2.26$feet

c. $0.37$feet

d. $2.32$feet

e. $0.43$feet

Short answer

The correct option is (e).

Step-by-step solution

Given information

The given data is

Explanation

The general equation is $\hat{y}=b_0+b_{1}x$

The computation of the constant $b_0$is noted in the computer output's row "Constant" and column "Coef":

$b_0=0.45374$

The computation of the slope $b_1$is mentioned in the computer output's row "Bounce" and column "Coef":

$b_1=-0.117160$

Substitute the values in the equation

role="math" localid="1654189474140" $=0.45374-0.117160x$

$\log y=0.45374-0.117160x$

Put the value of x

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

$=-0.36638$

Then take the exponential

$$\begin{gathered} \hat{y}={10}^{\log y} \\ \hat{y}={10}^{-0.36638} \\ \hat{y}=0.43 \end{gathered}$$

The option is (e).