Question

The value of a motorcycle changes according to the equation V=13,000(0.75)^t
, where V = value in dollars and t = time in years.

Use the dropdowns to complete the statements.


In the equation, the number 13,000 represents the
of the motorcycle. The value of the motorcycle is
at a rate of
per year.

What does V=15,000 mean in the context of this problem?

Is it possible for V=15,000 in the context of this problem?

What does a value of t = 2 mean in the context of this problem?

Answer 1

- 13,000 represents the initial value (the value at t = 0) of the motorcycle.
- The value of the motorcycle is decreasing (depreciating) at a rate of 25% per year (since 0.75 = 1 − 0.25).

What does V = 15,000 mean?
- It means the motorcycle is worth $15,000.

Is V = 15,000 possible here?
- No. According to the model the value starts at $13,000 and decreases for t ≥ 0, so it can never be $15,000 in this context.

What does t = 2 mean?
- t = 2 means 2 years after the starting time (2 years after purchase / after t = 0).