https://file.aiquickdraw.com/mathbot/file/1730525610270nvp8drg2.jpg

To solve this problem, we can use the exponential depreciation formula:

\[
V = P \times (1 - r)^t
\]

where:
- $ V $ is the value of the vehicle after $ t $ years,
- $ P $ is the initial purchase price of the vehicle,
- $ r $ is the annual depreciation rate,
- $ t $ is the number of years since the purchase.

### Given Values
- **Initial value, $ P $** = 20,700 dollars
- **Depreciation rate, $ r $** = 9% per year (or 0.09 in decimal form)
- **Time, $ t $** = 13 years

### Plugging in the Values
1. Substitute $ P = 20700 $, $ r = 0.09 $, and $ t = 13 $ into the formula:

\[
V = 20700 \times (1 - 0.09)^{13}
\]

2. Simplify $ (1 - 0.09) = 0.91 $:

\[
V = 20700 \times (0.91)^{13}
\]

3. Now calculate $ (0.91)^{13} $ and then multiply by 20,700.

Let’s go through these steps:

\[
(0.91)^{13} \approx 0.297
\]
\[
V \approx 20700 \times 0.297 \approx 6158
\]

### Final Answer
The approximate value of the vehicle after 13 years is **$6,158** (rounded to the nearest whole number).

Would you like more details on the calculation, or do you have any other questions?

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Here are some related questions you might find interesting:
1. How would the value change if the depreciation rate were different?
2. How can we adjust the formula if the depreciation rate is compounded monthly instead of yearly?
3. What is the formula for exponential growth, and how does it compare to depreciation?
4. How would the depreciation formula change if the rate decreased over time?
5. How can we calculate the total depreciation over a certain period?

**Tip:** When dealing with exponential decay, remember that the base (1 - r) is always less than 1, representing a decrease in value over time.

A vehicle purchased for $20700 depreciates at a rate of 9% per year. Determine the approximate value of the vehicle 13 years after purchase. Round to the nearest whole number.

Learn how to calculate the depreciated value of a vehicle purchased for $20700 after 13 years, using an annual depreciation rate of 9%. This problem covers key concepts in exponential functions and depreciation calculations. Suitable for high school students in Grades 9-12.

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