The value of a motorcycle changes according to the equation V(t)=5,000(1.03)tV(t)=5,000(1.03)t , where V(t) = value in dollars and t = time in years. Use the dropdowns to complete the statements. In the equation, the number 5,000 represents the of the motorcycle. What does V(t) = 9000 mean in the context of this problem? What does a value of t = 3 mean in the context of this problem?

Question

GPT-4o mini · Answer

In the equation $ V(t) = 5,000(1.03)^t $: - The number $ 5,000 $ represents the **initial value** of the motorcycle. This is the value of the motorcycle at time $ t = 0 $ (i.e., when it is first purchased). - The statement $ V(t) = 9,000 $ means that the value of the motorcycle is **$9,000** after a certain period of time. In other words, this indicates that at some time $ t $, the motorcycle has appreciated in value to $9,000. - A value of $ t = 3 $ means **3 years** have passed since the purchase of the motorcycle. In this context, it refers to the time duration for which the motorcycle's value has been changing, and you can use this to calculate the value of the motorcycle at that point in time using the provided equation.