To calculate the approximate value of a vehicle that depreciates at a rate of 8% per year, we can use the formula for exponential decay:

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

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, and
• $t$ is the number of years.

Given values:

• $P = 22400$ (initial value),
• $r = 0.08$ (8% depreciation rate),
• $t = 15$ (years).

Solution:

1. Substitute the values into the formula:

   $V = 22400 \times (1 - 0.08)^{15}$

2. Calculate the inside of the parentheses:

   $V = 22400 \times (0.92)^{15}$

3. Find $(0.92)^{15}$:

   $(0.92)^{15} \approx 0.275$

4. Multiply by the initial value:

   $V \approx 22400 \times 0.275$

5. Calculate the final answer:

   $V \approx 6160$

Conclusion:

The approximate value of the vehicle after 15 years is $6,160.

Would you like further details or have any questions?

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Here are five related questions to expand understanding:

1. How does changing the depreciation rate affect the vehicle’s value over time?
2. What would be the vehicle's value after 10 years instead of 15?
3. How would the vehicle's value change if it depreciated at 5% per year?
4. How does compound depreciation differ from simple depreciation?
5. What is the value of the vehicle if the depreciation rate is compounded monthly?

Tip: Exponential decay formulas are useful for any scenario with regular percentage decreases, such as the depreciation of assets.