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 correct model for depreciation is $V(t) = 39,000 \left( \frac{7}{8} \right)^t$, where the original value is multiplied by $\frac{7}{8}$ for each year t.

After T Years, the Value of a Wheelchair Conversion Van 78\frac { 7 } { 8 }87​

After T Years, the Value of a Wheelchair Conversion Van $\frac { 7 } { 8 }$