A new car is purchased for 22300 dollars. The value of the car depreciates at 10.25% per year. What will the value of the car be, to the nearest cent, after 6 years?

To calculate the value of the car after 6 years, we use the formula for exponential depreciation:

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

Where:
- $V$ is the value of the car after $t$ years,
- $P$ is the initial purchase price of the car,
- $r$ is the annual depreciation rate (in decimal form),
- $t$ is the number of years.

Given:
- $P = 22300$ dollars,
- $r = 10.25\%$ or $0.1025$,
- $t = 6$ years.

Now, substitute the values into the formula:

\[
V = 22300 \times (1 - 0.1025)^6
\]

\[
V = 22300 \times (0.8975)^6
\]

Now, calculate $0.8975^6$:

\[
0.8975^6 \approx 0.5656
\]

Then,

\[
V = 22300 \times 0.5656
\]

\[
V \approx 12603.88
\]

Therefore, the value of the car after 6 years will be approximately **$12,603.88**.

Would you like more details or have any questions?

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Here are 5 related questions to explore:
1. What will be the value of the car after 10 years?
2. How much value will the car lose after 6 years?
3. What would the value be if the depreciation rate was 8% instead of 10.25%?
4. How long will it take for the car’s value to depreciate to half its original value?
5. What is the total depreciation in dollars after 6 years?

**Tip:** For exponential decay problems, always ensure the depreciation rate is converted to decimal form by dividing the percentage by 100.

Calculate the depreciated value of a car purchased for $22,300 after 6 years, using a 10.25% annual depreciation rate. This example demonstrates the exponential decay formula and percentage-based depreciation, suitable for high school students in grades 9-12.

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