Chapter 1.2, Problem 18Q

To determine

The type of function that can be used to model the data and then to estimate the mileage after $1$ year.

Answer to Problem 18Q

Linear function is used to model the data and mileage after $1$ year would be $13800miles$ .

Explanation of Solution

Given information: A table containing data-values of time and distance is given.

Calculation:

Calculating the distance travelled per month,

  $\frac{2300-0}{2-0}=\frac{5750-2300}{5-2}=\frac{6900-5750}{6-5}=\frac{10350-6900}{9-6}=1150$

As the distance travelled each month is same in all cases, linear function can be used to model the data,

Slope intercept form: $y=mx+b$ ,

where $m=\frac{y_2-y_1}{x_2-x_1}$ ,

Distance travelled per month calculated before is itself the slope $m$ ,

When $x=0,y=0$

  $\Rightarrow y-\mathrm{int}ercept=0$

Substituting the values derived so far in slope-intercept form,

  $y=1150x$

Putting $x=12$ (as there are $12$ months in an year) to estimate mileage,

  $\begin{array}{l}y=1150(12)\\ \\ =13800\end{array}$

Thus, linear function is used to model the data and mileage after $1$ year would be $13800miles$ .