Question

A truck is bought at the price of $67,000. The price decreases at the rate of .30 every year (t). Which equation matches this exponential model?A) f(t) = 67(.70)tB) f(t) = 70(67,000)tC) f(t) = t(.70)67,000D) f(t) = 67,000(.70)t

Answer 1

Data:

Initial price: $67.000

Price decrease: .30 each year t

The general form of a model of exponential decrease is:

$f(t)=p_0(1-r)^t$

Where P0 is the initial price, r is the rate of decrease and t the number of periods.

Then, for the given situation you get the next equation:

$\begin{gathered} f(t)=67000(1-0.30)^t \\ f(t)=67000(.70)^t \end{gathered}$Then, the answer is the option D.