Chapter 1, Problem 26RE

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 26RE

the linear equation is $V=275t+2650$.

Explanation of Solution

Given information :

  $2015\text{ value }=\$4025$

Rate = $\$275$ increase per year

Formula used :

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

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

Since $2015\text{ value }=\$4025$ ,

So the point on linear equation is $\left(5,4025\right)$.

The increasing value per year = $\$275$.

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 $\$275$ ,so the equation

  $\begin{array}{l}V=mt+c\\ V=275t+c\text{ [substitute]}\end{array}$

Now find the value of $c$ , substitute $t=5,V=4025$

  $\begin{array}{l}V=275t+c\\ 4025=275\left(5\right)+c\text{ [substitute t}=5,V=12500]\\ c=2650\text{ [simplify}]\end{array}$

Thus, the linear equation is $V=275t+2650$.