Chapter 1.1, Problem 90E

To determine

Calculate the linear equation that gives the dollar value V of the product in terms of the year t .

Answer to Problem 90E

The linear equation that gives the dollar value V is $V=5.50t+106.5$ .

Explanation of Solution

Given: It is given in the question that the dollar value of a product in $2015$ is $\$156$ and the rate at which the product is expected to change during the next $5$ years is $\$5.50$ increase per year and ( let $t=15$ )

Concept Used:

In this, use the concept of understanding each and every variable so he to make a linear equation.

Calculation: Consider the solution to be of the form of $V=at+b$ and it have to be find the constant a and b then

Now since it is know that the rate of change is increased by $\$5.50$ ,we have $a=+5.50$ as it is the one which represents the rate of change with respect to t.

Now, findingb remains ,It is know that the value V at $t=9$ to be $\$156$ .

So, put $V=156$ and $t=9$ in $V=5.50t+b$

So,

  $\begin{array}{l}V=5.50t+b\\ 156=5.50(9)+b\\ b=156-49.5\\ b=106.5\end{array}$

So, the equation is $V=5.50t+106.5$ .

Conclusion:

The equation is $V=5.50t+106.5$ .