Question
Question 12 A)(6 points) The value of a motorcycle changes according to the equation V=13,000(0.75)tV=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?
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?
Answers
Answered by
GPT-4o mini
To complete the statements based on the equation \( V = 13,000(0.75)^t \):
1. In the equation, the number \( 13,000 \) **represents the initial value** of the motorcycle.
2. The value of the motorcycle is **decreasing** at a rate of **25%** per year (since \( 0.75 \) represents 75% of the value retained after each year, meaning it loses 25%).
Regarding \( V = 15,000 \):
- In the context of this problem, \( V = 15,000 \) means that the value of the motorcycle is being evaluated at a point where it is worth $15,000.
- It is **not possible for \( V = 15,000 \)** in the context of this problem. Since the initial value starts at \( 13,000 \) and decreases with time, the value will never exceed the initial value of $13,000.
For \( t = 2 \):
- A value of \( t = 2 \) means that **2 years have passed** since the purchase of the motorcycle. In this context, we would be evaluating the value of the motorcycle after 2 years of depreciation.
1. In the equation, the number \( 13,000 \) **represents the initial value** of the motorcycle.
2. The value of the motorcycle is **decreasing** at a rate of **25%** per year (since \( 0.75 \) represents 75% of the value retained after each year, meaning it loses 25%).
Regarding \( V = 15,000 \):
- In the context of this problem, \( V = 15,000 \) means that the value of the motorcycle is being evaluated at a point where it is worth $15,000.
- It is **not possible for \( V = 15,000 \)** in the context of this problem. Since the initial value starts at \( 13,000 \) and decreases with time, the value will never exceed the initial value of $13,000.
For \( t = 2 \):
- A value of \( t = 2 \) means that **2 years have passed** since the purchase of the motorcycle. In this context, we would be evaluating the value of the motorcycle after 2 years of depreciation.