Question

An equation for the depreciation of a car is given by y = A(1 – r)t , where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately how old is the car?
3.3 years
5.0 years
5.6 years
6.6 years

Answer 1

We have 1/2 = (0.9)^t. Taking logs:
t = ln(1/2) / ln(0.9) ≈ -0.693147 / -0.105361 ≈ 6.58 ≈ 6.6 years.

Answer: 6.6 years.