Algebra help needed

Question

A new truck loses value each year after it is purchased. The value of ford pickup truck was $24000 when new, but it been depreciating by about 10% per year.

A-Write an exponential equation for f(t) that models the value of the truck t years after purchased.

B-Find the value of the truck after 7 years

C-Estimate the number of years in which the value of truck is less than $5000

Answer 1

Part A

f(t) = 24000(0.90)^t

Part B

f(7) = 24000(0.90)⁷≈ $11479.13

Part C

24000(0.90)^t < 5000

(0.90)^t < 5/24

t*ln(0.90) < ln(5/24)

t < ln(5/24)/ln(0.90)

t ≈ 14.888

t ≈ 14 years (make sure to round down since f(t) needs to be less than 5000)

Hope this helped!

Answer 2

f(t) = 24000(0.90)^t

f(7) = 24000(0.90)⁷

5000 > 24000(0.90)^t