An equation for the depreciation of a car is given by y = A (1-r), where y = current value of the car, A = original cost, r = rate

of depreciation, and t = time, in years. The current value of a car is $12,282.50. The car originally cost $20,000 and

depreciates at a rate of 15% per year. How old is the car?

Step-by-step explanation:

y = A (1 - r) ^t ... y = value of car after t years ... A = original cost ... r = rate of depreciation ... t = time in years

y = 12,282.50

A = 20,000

r = 15% = 0.15

12,282.50 = 20,000 (1 - 0.15) ^t

12,282.50 / 20,000 = 0.85^t

0.614125 = 0.85^t

log 0.614125 = t * (log (0.85))

t = (log 0.614125) / (log 0.85)

t = 3 <== = 3 years old