Question

Chris purchased a used car for $19,700. The car depreciates exponentially by 10% per year. How much will the car be worth after 6 years? Round your answer to the nearest penny.

Answer 1

Given: Purchasing value of car = $19,700,

                 Rate of depriciation = 10% per year.

To find:  Final value of car after after 6 years.

Solution : Because rate of car is being depriciated exponential. So, we would exponential formula.

$A = Pe^{-kt}.$

Where, P is the purchase value, k is the rate of depriciation and t is the number of years.

Plugging values P = 19,700, r=10% that is 0.10 and t= 6 in above formula.

$A= 19,700e^{-0.10*6}$

$A= 19,700e^{-0.60}$

A= 19,700 (0.54881163609)

A= 10811.5892311.

Rounding to the nearest penny (two decimal places0.

A= 10811.59.

Therefore, Final value of car after after 6 years = $ 10811.59