Question

A car purchased for $34,000 is expected to lose value, or depreciate, at a rate of 6% per year. Using x for years and y for the value of the car, write the equation that models this situation. After how many years is the car first worth less than $21,000

Answer 1

The equation is y=34000(1-0.06)ˣ.

It will take nearly 8 years for the car to lose enough value to be worth less than $21,000.

Using 21,000 for y, we have
21000=34000(1-0.06)ˣ
21000=34000(0.94)ˣ

Dividing both sides by 34000:
21000/34000 = 34000(0.94)ˣ/34000
(21/34) = 0.94ˣ

Using logarithms to solve this,
$\log_{0.94}(\frac{21}{34})=x \\x=7.79 \approx8$