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The question asks for the value of a car after 6 years, given its initial value of $15,300 and an annual depreciation rate of 14.25%.

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

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

where:
- $ V(t) $ is the value of the car after $ t $ years,
- $ P $ is the initial value of the car (in this case, $15,300),
- $ r $ is the annual depreciation rate (14.25% or 0.1425 as a decimal),
- $ t $ is the number of years (6 years in this case).

Now, substituting the values:

\[
V(6) = 15,300 \times (1 - 0.1425)^6
\]

\[
V(6) = 15,300 \times (0.8575)^6
\]

Calculating this:

\[
V(6) \approx 15,300 \times 0.52215 \approx 7,990.90
\]

Thus, the value of the car after 6 years will be approximately **$7,990.90**.

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. How would the result change if the depreciation rate was compounded quarterly instead of yearly?
2. What is the total percentage depreciation over the 6 years?
3. How long would it take for the car’s value to drop below $5,000 at this depreciation rate?
4. What would be the car's value after 10 years instead of 6?
5. How would the car’s value differ if the initial price was higher, say $20,000?

**Tip:** In exponential decay models like this, small changes in the depreciation rate or time can lead to significant differences in the outcome.

A new car is purchased for 15300 dollars. The value of the car depreciates at 14.25% per year. What will the value of the car be, to the nearest cent, after 6 years?

Learn how to calculate the depreciated value of a car purchased for $15,300, which loses value by 14.25% annually, using exponential decay formulas. Follow the step-by-step solution to find the car's value after 6 years, rounded to the nearest cent. Ideal for high school students studying exponential decay in mathematics.

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