Question
A car valued at $10,000 loses 15 percent of its value each year. What is the initial amount for your function? What is the common ratio for this problem?
Answers
GPT-4o mini
To model the value of the car over time, we can use the concept of exponential decay, as the car loses a certain percentage of its value each year.
1. **Initial Amount:**
The initial amount (or starting value) of the car is $10,000.
2. **Common Ratio:**
The car loses 15% of its value each year, which means it retains 85% of its value after one year. Therefore, the common ratio can be calculated as:
\[
1 - 0.15 = 0.85
\]
So, to summarize:
- The initial amount for your function is **$10,000**.
- The common ratio is **0.85**.
Thus, the value of the car after \( t \) years can be expressed as:
\[
V(t) = 10000 \times (0.85)^t
\]
1. **Initial Amount:**
The initial amount (or starting value) of the car is $10,000.
2. **Common Ratio:**
The car loses 15% of its value each year, which means it retains 85% of its value after one year. Therefore, the common ratio can be calculated as:
\[
1 - 0.15 = 0.85
\]
So, to summarize:
- The initial amount for your function is **$10,000**.
- The common ratio is **0.85**.
Thus, the value of the car after \( t \) years can be expressed as:
\[
V(t) = 10000 \times (0.85)^t
\]