In the equation \( V = 13,000(0.75)^t \), the number 13,000 represents the initial value of the motorcycle. The value of the motorcycle decreases at a rate of 25% per year (since \( 0.75 \) represents 75% of the value remaining after one year, meaning it loses 25% of its value).
What does \( V = 15,000 \) mean in the context of this problem?
In this context, \( V = 15,000 \) would imply that the motorcycle’s value is $15,000. However, based on the equation provided, the maximum value that the motorcycle can have when it is new is $13,000. Therefore, it is not possible for \( V = 15,000 \) in this context because the value of the motorcycle will only decrease from the initial value of 13,000, and would never exceed this value.
What does a value of \( t = 2 \) mean in the context of this problem?
A value of \( t = 2 \) means that 2 years have passed since the motorcycle was purchased. It represents the time in years after the motorcycle was bought, used to determine its current value based on the depreciation model provided by the equation. Specifically, it can be used to calculate the value of the motorcycle after 2 years by substituting \( t \) with 2 in the equation.