Question
car enthusiast learns that a particular model of car, which costs $43,330 new, loses 17% of its value every year. How much will the car be worth in 9 years?
If necessary, round your answer to the nearest cent.
If necessary, round your answer to the nearest cent.
Answers
GPT-4o mini
To calculate the value of the car after 9 years, we need to know the depreciation formula for the car's value over time. The formula for the value of the car after a certain number of years is given by:
\[
V = P(1 - r)^t
\]
where:
- \( V \) is the value after \( t \) years,
- \( P \) is the initial value of the car,
- \( r \) is the depreciation rate (expressed as a decimal),
- \( t \) is the number of years.
In this case:
- \( P = 43330 \)
- \( r = 0.17 \) (since 17% as a decimal is 0.17)
- \( t = 9 \)
Now we can substitute these values into the formula:
\[
V = 43330(1 - 0.17)^9
\]
Calculating \( 1 - 0.17 \):
\[
1 - 0.17 = 0.83
\]
Now raise it to the power of 9:
\[
0.83^9 \approx 0.214394
\]
Now multiply this by the initial value of the car:
\[
V = 43330 \times 0.214394 \approx 9283.74
\]
Thus, the value of the car after 9 years is approximately **$9,283.74**.
\[
V = P(1 - r)^t
\]
where:
- \( V \) is the value after \( t \) years,
- \( P \) is the initial value of the car,
- \( r \) is the depreciation rate (expressed as a decimal),
- \( t \) is the number of years.
In this case:
- \( P = 43330 \)
- \( r = 0.17 \) (since 17% as a decimal is 0.17)
- \( t = 9 \)
Now we can substitute these values into the formula:
\[
V = 43330(1 - 0.17)^9
\]
Calculating \( 1 - 0.17 \):
\[
1 - 0.17 = 0.83
\]
Now raise it to the power of 9:
\[
0.83^9 \approx 0.214394
\]
Now multiply this by the initial value of the car:
\[
V = 43330 \times 0.214394 \approx 9283.74
\]
Thus, the value of the car after 9 years is approximately **$9,283.74**.