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 → $\frac{log 0.48}{log 0.9}$ = t
Plug into the calculator →  6.966 = t

Answer: A