Question

Sam bought a used car for $8,000. He boasted that he got a great deal since the value of the car two years ago

(when it was new) was $15,000. His friend, Derek, was skeptical, stating that the value of a car typically depreciates
about 25% per year, so Sam got a bad deal.
a. Use Derek’s logic to write a formula for the value of Sam’s car. Use t for the total age of the car in years.

Answer 1

`V(t) = 15,000*(0.75)^t`

Explanation:

The initial value is $15,000, and if it depreciates 25% per year, that means that for each year the value will be 0.75 of the value of the previous year. The next year, the value will be 0.75 of the previous, which will be o.75x0.75 of the initial value, or (0.75)².

So, for t years:

`V(t) = 15,000*(0.75)^t`