Question

The value of a newly purchased motorcycle will decrease over time. The value of the motorcycle can be modeled by the following function: V(t)=2,000+12,000(0.62)^2t where t is measured in years since the motorcycle was purchased.When t=0, the value of the motorcycle is _____ dollars.

a) $2,000
b) $4,000
c) $14,000
d) $26,000

As time increases, 12,000(0.62)^2t gets closer and closer to ____. So, V(t) gets closer and closer to _____.
a) 0; $2,000
b) 0; $12,000
c) 12,000; $14,000
d) 12,000; $26,000

Answer 1

When t = 0, the value of the motorcycle is $2,000. As time increases, 12,000(0.62)^2t gets closer to 0 and V(t) gets closer to $2,000.

Step-by-step explanation:

To find the value of the motorcycle when t = 0, we need to substitute t = 0 into the function V(t).

V(t) = 2,000 + 12,000(0.62)^2t

When t = 0, the value of the motorcycle is:

V(0) = 2,000 + 12,000(0.62)^2(0)

V(0) = 2,000 + 0

V(0) = 2,000

Therefore, the value of the motorcycle when t = 0 is $2,000.

As time increases, 12,000(0.62)^2t gets closer and closer to 0. So, V(t) gets closer and closer to 2,000.

Therefore, the answer is:

• a) $2,000
• b) 0; $2,000