Chapter 1.3, Problem 92E

To determine

To write a linear equation that gives the dollar value of product.

Answer to Problem 92E

  $\boxed{V=4.50t+97.5}$

Explanation of Solution

Given information:

You are given the dollar value of a product in $2013$ and the rate at which the value of the product is expected to change during the next $5$ years. Use this information to write a linear equation that gives the dollar value of the product in terms of the year $t$ .(let $t=13$ represent $2013$ )

  $\begin{array}{l}2013Value\\ \$156\end{array}$$\begin{array}{l}Rate\\ \$4.50increase/year\end{array}$

Calculation:

Let $t=13$ represent $2013$ and $V=156$ is the value of product in year $2013$ . It is given that product is expected to increase $\$4.50/year$ up to next $5$ years.

Since the rate is decreased means slope will be positive $m=4.50$ .

The equation of line with slope $m=4.50$ passes through points $\left(13,156\right)$ is,

  $\begin{array}{l}V-156=4.50\left(t-13\right)\\ V-156=4.50t-58.5\\ V=4.50t-58.5+156\\ V=4.50t+97.5\end{array}$

Hence equation of line is $\boxed{V=4.50t+97.5}$