Question

Joshua just purchased a 4-year-old car for $12,000. He was told that this make and model depreciates exponentially at a rate of 5.8% per year. What was the original price to the nearest hundred dollars?

Answer 1

`$15000`

Explanation:

After 4 years, the car is worth `$12000`.
Work backwards.

`3` `"years"=12000 xx 1.058= $12696`

`2` `"years"= 12696 xx 1.058= $13432.368`

`1` `"year"= 13432.368 xx 1.058= $14211.445344`

Original: `14211.445344 xx 1.058= $15035.709174`

to nearest `$100`
`=$15000`

-Fish

Answer 2

Write an equation to satisfy the word problem:

`12000=x(1-0.058)^(4)`

Solve:

`0.7874x=12000`

`x~~15240.03`

The price was approximately `$15240.03`, and to the nearest hundred dollars is `$15200`.