Question

A new car is purchased for 24800 dollars. The value of the car depreciates at 7.25% per year. To the nearest tenth of a year, how long will it be until the value of the car is 9000 dollars?

Answer 1

Answer: 13.5 years

We can represent the situation with the equation 9000=24800*(0.9275)^x. Since this is an exponential decay question (depreciation), we had to subtract 7.25% from 1 to get the 0.9275

When we divide both sides by 24800, we get 45/125=0.9275^x.

You could solve with a graphing calculator (a great online version is (Desmos), or simply use log argument (45/124)/log base (0.9275) to get about 13.468, which round to 13.5.