Chapter 9.6, Problem 25E

a.

To determine

To find: A model function that given $N$ as function of $t$ .

Answer to Problem 25E

  $N=3.682\sin \left[0.775\left(t-0.907\right)\right]+20.368$ .

Explanation of Solution

Given information:

Below table shows the number of employees $N$ (in thousand) at a sporting goods company each year for $11$ years. $t=1$ , represents first year and so on.

  

Calculation:

Below table shows the number of employees $N$ (in thousand) at a sporting goods company each year for $11$ years. $t=1$ , represents first year and so on.

  

Plotting the scatter plot for the given data.

  

Scatter plot appears sinusoidal. Performing sinusoidal regression using a graphing utility.

  

  

The model appears to be a good fit.

So, the model will be given by −

  $N=3.682\sin \left[0.775\left(t-0.907\right)\right]+20.368$ .

Hence, desired function is $N=3.682\sin \left[0.775\left(t-0.907\right)\right]+20.368$ .

b.

To determine

To find: The number of employees in the company in $12$ th year.

Answer to Problem 25E

  $23065$ employees.

Explanation of Solution

Given information:

Same as part $a$ of this exercise.

Calculation:

From part $a$ of this exercise,

  $N=3.682\sin \left[0.775\left(t-0.907\right)\right]+20.368$

Where $N$ is number of employee (in thousands) and $t$ is number of years.

Put $t=12$ ,

  $\begin{array}{l}N=3.682\sin \left[0.775\left(12-0.907\right)\right]+20.368\\ \Rightarrow N=23.065\text{ thousands}\\ \Rightarrow N=23065\end{array}$

Hence, in $12$ th year there would be $23065$ employees in the company.