Chapter 3.3, Problem 74ES

Suppose that a new car is purchased for $\text{\$}20,000$ and depreciates by $15\%$ each year.

(a) Explain why the dollar value $V$ of the car $t$ years after the date of purchase can be modeled by the function $V=20,000{\left(0.85\right)}^t$ .

(b) For the model in part (a) determine how rapidly the car is losing value (in dollars per year) $5$ years after the date of purchase.