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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 :

wall88
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:

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

[tex]f(t)=a(r)^{t}[/tex]

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 = [tex]\frac{350}{500}=0.70[/tex]

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

[tex]a_{n}=a(r)^{n}[/tex]

[tex]a_{n}=500(0.70)^{n}[/tex] where n is the time in years.

For t = 5 years

[tex]a_{5}=500(0.70)^{5}[/tex]

[tex]a_{5}=500(0.168)[/tex]

[tex]a_{5}=84.035[/tex]

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

Option A is the answer.

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