Chapter 1.3, Problem 95E

To determine

To write: amount linear equation giving the value V of the equipment during 5 years of its use.

Answer to Problem 95E

  $V\left(t\right)=-175t+875$, $0\le t\le 5$

Explanation of Solution

Given:

The equipment was purchased at $875 and after 5 years it will be discarded.

Concept Used:

Two-point form of equation of line:

The equation of line passing through two point $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given by $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$ where $x_1\ne x_2$ .

Let V represents the value of the equipment for the year t .

Now it is given that the equipment was purchased at $875. That is for $t=0$ , $V=875$ . It can be written as $\left(0,875\right)$ .

Also, after 5 years equipment will be discarded that is its value will become 0. That is for $t=5$ , $V=0$ . It can be written as $\left(5,0\right)$ .

Now, to find the required equation of line use two point form of equation of line and substitute $\left(x_1,y_1\right)=\left(0,875\right)$ and $\left(x_2,y_2\right)=\left(5,0\right)$

  $\begin{array}{c}V-875=\left(\frac{0-875}{5-0}\right)\left(t-0\right)\\ V-875=\left(-\frac{875}{5}\right)t\\ V-875=-175t\\ V=-175t+875\end{array}$

Conclusion:

The value V of the equipment during 5 years of its use is given by $V\left(t\right)=-175t+875$, $0\le t\le 5$