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?
$84
$119
$164
$222

Answer 1

It starts at $500, then decreases by 30% so just multiply 500 by .7, then multiply the answer by .7, and so on until you get to $84.

Answer 2

Answer:

After 5 years cost of the dirt bike will be $84.

Option A is the answer.

Step-by-step explanation:

The value of a dirt bike decreases by 30% each year. If the present cost of the dirt bike is $500.

Then the function which defines the decrease in cost of the bike will be

$f(t)=a(r)^{t}$

where a = $500

After one year decrease in the cost of the bike will be = 500×0.30 = $150

The cost of the bike next year will be = 500-150 = $350

So the sequence for the cost every year will be 500, 350..........

Now the common ratio of the sequence will be = $\frac{350}{500}=0.70$

Now we can form the explicit formula for this geometric sequence as

$a_{n}=a(r)^{n}$

$a_{n}=500(0.70)^{n}$ where n is the time in years.

For t = 5 years

$a_{5}=500(0.70)^{5}$

$a_{5}=500(0.168)$

$a_{5}=84.035$

Therefore, after 5 years cost of the dirt bike will be $84.

Option A is the answer.