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}
$
Tuesday, January 19, 2016
College Algebra, Chapter 2, 2.4, Section 2.4, Problem 72
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