Question

A new car sells for $25,000. The value of the car decreases by 17% annually. After how many years will the car be worth less than $10,000. Choose the best answer. (4.2)


a. after 4 years


b. after 6 years


c. after 8 years


d. not enough information

Answer 1

Let a = car's age in years and v = value of car.

v = 25000(1 - 0.17)^a 

v = 25000(0.83)^a 

v = 25000(0.83)^a 

We need to find a.

Let v = 10,000

10,000 = 25000(0.83)^a

The value of a is about 4.91758.

Round off to the nearest whole number we get 5.

Answer is after more than 4 years but less than 6 and 8.