Chapter 1.1, Problem 91E

To determine

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

Answer to Problem 91E

The linear equation that gives the dollar value V is $V=-2000t+38400$ .

Explanation of Solution

Given: It is given in the question that the dollar value of a product in $2015$ is $\$20400$ and the rate at which the product is expected to change during the next $5$ years is $\$2000$ decrease 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 decreased by $2000$ ,we have $a=-2000$ 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 $20400$ .

So, put $V=20400$ and $t=9$ in $V=-2000t+b$

So,

  $\begin{array}{l}V=-2000t+b\\ 20400=-2000(9)+b\\ b=20400+18000\\ b=38400\end{array}$

So, the equation is $V=-2000t+38400$ .

Conclusion:

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