### Home > CAAC > Chapter 13 > Lesson 13.OF2-S > Problem 7-138

A rule-of-thumb used by car dealers is that the trade-in value of a car decreases by 20% of its value each year.

Explain how the phrase “decreases by 20% of its value each year” tells you that the trade-in value varies exponentially with time (i.e., can be represented by an exponential function).

“Decreases by

” means that you multiply by each year.A sequence with a multiplier is geometric and has an exponential rule. Suppose the initial value of your car is $23,500. Write an equation expressing the trade-in value of your car as a function of the number of years from now.How much will your car be worth in four years?

Use the equation that you found in part (b).

In how many years will the trade-in value of your car be $6000?

Divide by

first then take the log of both sides. If your car is really 2.7 years old now, what was its trade-in value when it was new?

This was

years ago, so let in the equation.