Chapter 1, Problem 27RE

To determine

To find : the linear equation that gives the dollar value $V$ of the product in terms of the year $t$.

Answer to Problem 27RE

the linear equation is $V=42.70t+412$.

Explanation of Solution

Given information :

  $2015\text{ value }=\$625.50$

Rate = $\$42.70$ increase per year

Formula used :

The equation of line is $y=mx+c$.

Calculation: let $t=5$ represent $2015$ ,

Since $2015\text{ value }=\$625.50$ ,

So the point on linear equation is $\left(5,625.50\right)$.

The increasing value per year = $\$42.70$.

The value increase per year so it is the slope of the linear equation.

Now, substitute the value of slope in the equation,

Since slope of the line $\$42.70$ ,so the equation

  $\begin{array}{l}V=mt+c\\ V=42.70t+c\text{ [substitute]}\end{array}$

Now find the value of $c$ , substitute $t=5,V=625.50$

  $\begin{array}{l}V=42.70t+c\\ 625.50=42.70\left(5\right)+c\text{ [substitute t}=5,V=12500]\\ c=412\text{ [simplify}]\end{array}$

Thus, the linear equation is $V=42.70t+412$.