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

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Verified Answer :

wall88 wall88 · Answer 1 · 2016-11-14T14:47:21-05:00

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.

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eudora eudora · Answer 2 · 2019-07-15T17:32:40-04:00

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 = @@MATH_TOKEN_1@@

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

@@MATH_TOKEN_2@@

@@MATH_TOKEN_3@@ where n is the time in years.

For t = 5 years

@@MATH_TOKEN_4@@

@@MATH_TOKEN_5@@

@@MATH_TOKEN_6@@

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

Option A is the answer.