Question

Depreciation (the decline in cash value) on a car can be determined by the formula V =C(1-r)t , where V is the value of the car after t years, C is the original cost, and r is the rate of depreciation. If a car’s cost, when new, is $17,500, the rate of depreciation is 20%, and the value of the car now is $5,000, how old is the car to the nearest tenth of a year?

Answer 1

5.6 years

Explanation:

The exponential depreciation formula for the value of a car can be solved for time by making use of logarithms.

__

given

We are given ...

V = C(1 -r)^t . . . . . where C = $17,500, r = 20%, V = $5,000

and we are asked to find t.

solution

Substituting the given values, we have ...

5000 = 17500(1 -0.20)^t

5000/17500 = 0.80^t . . . . . . . divide by 17500

log(2/7) = t×log(0.80) . . . . . simplify and take logarithms

t = log(2/7)/log(0.80) ≈ 5.614

The car is about 5.6 years old when its value is $5000.