Chapter 1, Problem 25RE

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 25RE

the linear equation is $V=850t+8250$.

Explanation of Solution

Given information :

  $2015\text{ value }=\$12,500$

Rate = $\$850$ increase per year

Formula used :

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

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

Since $2015\text{ value }=\$12,500$ ,

So the point on linear equation is $\left(5,12500\right)$.

The increasing value per year = $\$850$.

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 $850$ ,so the equation

  $\begin{array}{l}V=mt+c\\ V=850t+c\text{ [substitute]}\end{array}$

Now find the value of $c$ , substitute $t=5,V=12500$

  $\begin{array}{l}V=850t+c\\ 12500=850\left(5\right)+c\text{ [substitute t}=5,V=12500]\\ c=8250\text{ [simplify}]\end{array}$

Thus, the linear equation is $V=850t+8250$.