Exponential question

Question

Anne bought a new car for $35 000 and sold it five years later for $18 475. Assume that the value of the vehicle depreciates exponentially. Calculate the annual rate of depreciation.

Answer 1

The car depreciates a fixed rate per year. Let P denote the price of a car with P_o being the original price of $35,000. We can model this scenario using the following equation:

P = P_o(1-r)^t

Every year (t)our car depreciated by a fixed amount (r). Knowing our car has depreciated for 5 years, we rearrange the equation to solve for r

18,475 = 35,000(1-r)⁵

18,475/35,000 = (1-r)⁵

(18,475/35,000)^1/5 = 1-r

0.88 = 1-r

r = .12 or 12%

Hope this helps!