After t years, the value of a car that originally cost $\$$ 17,000 depreciates so that each year it is worth $\frac { 3 } { 4 }$ of its value for the previous year. Find a model for V(t), the value of the car after t years.
A)V(t)= 17,000 $\left( \frac { 3 ^ { t } } { 4 } \right)$
B)V(t)= 17,000t $\left( \frac { 3 } { 4 } \right)$
C)V(t)= 17,000 $\left( \frac { 3 } { 4 } \right) ^ { t }$
D)V(t)= 17,000 $\left( \frac { 3 } { 4 ^ { t } } \right)$
E)V(t)= 17,000t $\left( \frac { 3 } { 4 } \right) ^ { t }$

Question

Quizplus · Accepted Answer

The correct model for depreciation in this case is $V(t) = 17,000 \left( \frac{3}{4} \right)^t$, where each year the car's value is multiplied by $\frac{3}{4}$, indicating a 25% depreciation annually.

After T Years, the Value of a Car That Originally $\$$