Question

Doug bought a new car for 25,

000. He estimates his car will depreciate, or lose of value, at a rate of 20% per year. The value of his car is molded by the equation v=p(1-r)^t, where v is the value of the car, p is the price paid, r is the annual rate of depreciation, and t is the number of years he had owned the car. According to the model, what will be the approximate value of his car after 4 1/2 years?

Answer 1

B on edge

Explanation:

9,159

Answer 2

This is exponential decay which can be expressed as:

y=ab^t, y=final value, a=initial value, b=rate, t=time

In this case a=25000, r=(100-20)/100=0.8 so

y=25000(0.8^t), so in 4.5 years...

y=25000(0.8^4.5)

y≈$9158.93 (to nearest cent)