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?

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Answer 1 · 2017-10-11T19:36:09

Approximately $$ 84.04$ $$84.04$

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

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

So:

$500 (0.7) (0.7) (0.7) (0.7) (0.7) = 500 {(0.7)}^{5} = 500 (0.16807) = 84.035$ $500(0.7)(0.7)(0.7)(0.7)(0.7)=500(0.7)^5=500(0.16807)=84.035$

So approximately $$ 84.04$ $$84.04$

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

$y = a b^{x}$ $y=ab^x$ where $a =$ $a=$ initial amount,

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

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

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