Question

Doug bought a new car for $25,000. He estimates his car will depreciate, or lose value, at a rate of 20% per year. The value of his car is modeled by the equation V = P(1 – r)t, where V is the value of the car, P is the price he paid, r is the annual rate of depreciation, and t is the number of years he has owned the car. According to the model, what will be the approximate value of his car after 4 and one-half years?
$2,500
$9,159
$22,827
$23,791

Answer 1

V = 25,000(0.8)^{4.5}.

Compute 0.8^4 = 0.4096 and sqrt(0.8) ≈ 0.8944, so 0.8^{4.5} ≈ 0.4096·0.8944 ≈ 0.36634.

V ≈ 25,000·0.36634 ≈ $9,159.

Answer: $9,159.