Doug bought a new car for 25 dollars comma 000 He estimates his car will depreciate, or lose value, at a rate of 20 percent per year. The value of his car is modeled by the equation cap v is equal to cap p times open paren 1 minus r close paren to the t th power , where cap v is the value of the car, cap 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 1 half years?
Use the depreciation model with p = $25,000, r = 0.20, and t = 4.5: v = 25,000(1 − 0.20)^4.5 = 25,000(0.8)^4.5 ≈ $9,159. Therefore, the approximate value is $9,159, choice A.
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