Answer :
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.