Question

The equation V(t) = 12,000(0.75)^t represents the value of a motorcycle

t years after it was purchased. Which statement is true?

(1) The motorcycle cost $9000 when purchased.

(2) The motorcycle cost $12,000 when purchased.

(3) The motorcycle's value is decreasing at a rate of 75% each year.

(4) The motorcycle's value is decreasing at a rate of 0.25% each year.

Answer 1

(2) The motorcycle cost $12,000 when purchased.

Explanation:

In the standard exponential equation, y = ab^x, a is the original value.

Since the equation is V(t) = 12,000(0.75)^t, a is 12,000.

This means that the original value was 12,000.

So, the motorcycle cost $12,000 when it was first purchased.

The correct answer is (2) The motorcycle cost $12,000 when purchased.