After t years,the value of a wheelchair conversion van that originally cost $39,000 depreciates so that each year it is worth $\frac { 7 } { 8 }$ of its value for the previous year.Find a model for V(t),the value of the van after t years.
A) $V ( t ) = - 39,000 \left( - \frac { 7 } { 8 } \right) ^ { t }$
B) $V ( t ) = 39,000 \left( - \frac { 7 } { 8 } \right) ^ { t }$
C) $V ( t ) = - 39,000 \left( \frac { 7 } { 8 } \right) ^ { t }$
D) $V ( t ) = 39,000 \left( \frac { 7 } { 8 } \right) ^ { t }$
E) $V ( t ) = 39,000 \left( \frac { 7 } { 8 } \right) ^ { - t }$

Question

After t years,the value of a wheelchair conversion van that originally cost $39,000 depreciates so that each year it is worth $\frac { 7 } { 8 }$ of its value for the previous year.Find a model for V(t),the value of the van after t years. ​
A) $V ( t ) = - 39,000 \left( - \frac { 7 } { 8 } \right) ^ { t }$
B) $V ( t ) = 39,000 \left( - \frac { 7 } { 8 } \right) ^ { t }$
C) $V ( t ) = - 39,000 \left( \frac { 7 } { 8 } \right) ^ { t }$
D) $V ( t ) = 39,000 \left( \frac { 7 } { 8 } \right) ^ { t }$
E) $V ( t ) = 39,000 \left( \frac { 7 } { 8 } \right) ^ { - t }$

Quizplus · Accepted Answer

The model for depreciation is $V(t) = P(1 - r)^t$, where $P$ is the initial value, $r$ is the rate of depreciation, and $t$ is time. Here, $P = 39,000$ and $r = \frac{1}{8}$, so the value each year is $\frac{7}{8}$ of its value the previous year, correctly represented as $V(t) = 39,000 \left( \frac{7}{8} \right)^t$.

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