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

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.