Chapter 1.3, Problem 96E

To determine

To write: amount linear equation giving the value V of the equipment during 10 years of its use.

Answer to Problem 96E

  $V\left(t\right)=-2200t+24000$, $0\le t\le 10$

Explanation of Solution

Given:

The equipment was purchased at $24,000 and after 10 years its value will be $2000.

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 $24,000. That is for $t=0$ , $V=24000$ . It can be written as $\left(0,24000\right)$ .

Also, after 10 years equipment’s value will become $2000. That is for $t=10$ , $V=2000$ . It can be written as $\left(10,2000\right)$ .

Now, to find the required equation of line use two point form of equation of line and substitute $\left(x_1,y_1\right)=\left(0,24000\right)$ and $\left(x_2,y_2\right)=\left(10,2000\right)$

  $\begin{array}{c}V-24000=\left(\frac{2000-24000}{10-0}\right)\left(t-0\right)\\ V-24000=\left(-\frac{22000}{10}\right)t\\ V-24000=-2200t\\ V=-2200t+24000\end{array}$

Conclusion:

The value V of the equipment during 10 years of its use is given by $V\left(t\right)=-2200t+24000$, $0\le t\le 10$ .