Question

The value of a dirt bike decreases by 30% each year. If you purchased this dirt bike today for $500, to the nearest dollar, how much would the bike be worth 5 years later?

Answer 1

Approximately `$84.04`

Explanation:

Decreasing by `30%` is the same as taking `70%` of the previous price.

So the price starts at `500` and gets multiplied by `0.7` (because that is `70%` as a decimal) five times (for each year).

So:

`500(0.7)(0.7)(0.7)(0.7)(0.7)=500(0.7)^5=500(0.16807)=84.035`

So approximately `$84.04`

You can generally model exponential decay/growth by using the equation:

`y=ab^x` where `a=`initial amount,

`b=`growth factor (1 plus the percent as a decimal) or decay factor (1 minus the percent as a decimal)

`x=`time and `y=`final amount after the growth/decay

In your problem `a=500`, `b=0.7`, `x=5`, and `y=84.035`