College Algebra, Chapter 2, 2.4, Section 2.4, Problem 72

A small business buys a computer for $\$ 4000$. After 4 years, the value of the computer is expected to be $\$ 200$. If $V$ is the value of the computer at time $t$, then a linear equation is used to relate $V$ and $T$.

a.) Find a linear equation that relates $V$ and $t$.

b.) Sketch a graph of this linear equation.

c.) What do the slope and $V$ intercept of the graph represent?

d.) Find the depreciated value of the computer 3 years from the date of purchase.

a.) By observation, the $V$ intercept is $\$ 4000$ because it is the initial value of the computer even if it has not utilized yet. Also, if the value of the computer depreciate after 4 years, then the slope can be computed as

$\displaystyle \frac{200 - 4000}{4} = -950$. Thus, the equation is..

$V = -950t + 4000$

b.)








The values $4000$ and $\displaystyle \frac{80}{19}$ are the $V$ and $t$ intercept respectively.

c.) The slope represents the depreciating rate of the value of the computer as years pass by. On the other hand, $V$-intercept represents the initial value of the computer.

d.) @ $t = 3$ years


$\begin{equation} \begin{aligned} V =& -950(3) + 4000 \\ \\ V =& \$ 1150 \end{aligned} \end{equation}$