Chapter 6.7, Problem 24E

To determine

Whether the data show an exponential relationship, then write a function tht models the data.

Answer to Problem 24E

The linear function that models the data is $y=-0.43x+11.43$ .

Explanation of Solution

Given information :

The given data is $\begin{array}{ccccccc}x& -20& -13& -6& 1& 8& 15\\ y& 25& 19& 14& 11& 8& 6\end{array}$ .

Calculation :

Make a scatter plot of the data. The scatter plot of the data is drawn below:

  

Therefore, the data appears as linear.

Choose any two points to write a model, such as $\left(1,\text{ 11}\right)$ and $\left(8,\text{ 8}\right)$ . Substitute the coordinate of these points into $y=ax+b$ . Therefore,

  $11=a+b$ …… (1)

  $8=8a+b$ …… (2)

Subtract equation (1) from equation (2):

  $\begin{array}{l}8-11=8a+b-\left(a+b\right)\\ -3=7a\\ -\frac{3}{7}=a\\ -0.43=a\end{array}$

Substitute $-0.43=a$ in equation (1) and solve for b:

  $\begin{array}{l}11=-0.43+b\\ 11+0.43=b\\ 11.43=b\end{array}$

So, the linear function that models the data is

  $y=-0.43x+11.43$

Hence,

The linear function that models the data is $y=-0.43x+11.43$ .