Chapter 1, Problem 13CR

To determine

To find:

Linear equation that gives the dollar values $V$ of the product in terms of year.

Answer to Problem 13CR

Linear equation that gives the dollar value $V$ of the product in terms of the year $t$ is $V=\$1580t+\$14220$ .

Explanation of Solution

Given information:

Value: $\$15800$

Rate: $\$1580$ increase per year

  $t=18$

Calculation:

Consider the dollar value of a product in $2018$ is $\$15800$ , and, the rate of change increases per

year is $\$1580$ .

Need to write a linear equation that gives the dollar value $V$ of the product in terms of the year $t=18$ , where represents the year $2018$ .

In general, the general form of the linear equation is $y=mx+b$ ,

Where,

  $m:$ means the slope or rate of change

  $b:$ means the $y-$ intercept or the initial value.

Here, the rate of change is $\$1580$ increases per year.

Assume $b$ be the initial dollar value of the product or the dollar value of the product in the year $2018$ .

Then, the linear equation will follow the form,

.$V=\$1580t+b$

Next solve for $b$

Given that the dollar value of a product in $2018$ is $\$15800$ , that means $V=\$15800$ .

The value of $t$ corresponds to the year $2018$ is $8$ , because, $t=18$ represents the year $2018$ .

Substitute $V=\$15800,t=18,V=\$1580t+b$

  $\begin{array}{l}\$15800=\$1580\left(1\right)+b\\ \$15800=\$1580+b\\ \$14220=b\end{array}$

Initial dollar value of the product is $\$14220$

Finally, substitute $\$14220=b$ in $V=\$1580t+b$

Then, $V=\$1580t+\$14220$

Therefore, linear equation that gives the dollar value $V$ of the product in terms of the year $t$ is $V=\$1580t+\$14220$ .