Question

A car with a cost of $25,000 is decreasing in value at a rate of 10% each year. The function g(t)= 25,000(0.9)^t gives the value of the car after t years. When will the value of the car be about $12,000? A) after 7 years B) after 9 years C) after 13 years

Could you also explain how to do it?

Answer 1

12,000 = 25,000
`(0.9)^(t)`
Divide both sides by 25,000 → 0.48 =
`(0.9)^(t)`
Convert to log form →
`log_(0.9)` 0.48 = t
Use the change of base formula →
`(log 0.48)/(log 0.9)` = t
Plug into the calculator → 6.966 = t

Answer: A