To calculate the value of the car after 6 years with an annual depreciation rate of 14.25%, we use the formula for exponential decay:

$V = P \cdot (1 - r)^t$

Where:

• $V$ is the value of the car after $t$ years,
• $P = 15300$ is the initial value of the car,
• $r = 0.1425$ is the annual depreciation rate (14.25% as a decimal),
• $t = 6$ is the time in years.

Step-by-step solution:

1. Substitute the given values into the formula: $V = 15300 \cdot (1 - 0.1425)^6$

2. Simplify the base of the exponent: $V = 15300 \cdot (0.8575)^6$

3. Calculate $(0.8575)^6$: $(0.8575)^6 \approx 0.50329$

4. Multiply by the initial value: $V = 15300 \cdot 0.50329 \approx 7700.34$

Final Answer:

The value of the car after 6 years will be $7700.34.

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Do you have any questions or need further clarification? 😊
Here are 5 related questions you might find useful:

1. What would the car's value be after 10 years with the same depreciation rate?
2. How does changing the depreciation rate affect the value over time?
3. Can you calculate the number of years it takes for the car’s value to drop below $5000?
4. What would the car’s value be after 6 years if the depreciation rate was compounded monthly instead of yearly?
5. What is the formula for calculating depreciation with a different model, such as straight-line depreciation?

Tip: Always convert percentages to decimals when plugging them into formulas!