To solve this problem:

Given:

• Initial value of the car: $8000
• Annual depreciation rate: 25%
• Time: 3 years

The value of the car decreases exponentially, so the formula to calculate the car's value after $t$ years is:

$V = V_0 \times (1 - r)^t$

Where:

• $V_0$ is the initial value ($8000$),
• $r$ is the annual depreciation rate ($0.25$),
• $t$ is the number of years ($3$).

Substituting the values:

$V = 8000 \times (1 - 0.25)^3$

$V = 8000 \times (0.75)^3$

$V = 8000 \times 0.421875$

$V = 3375$

Final Answer:

The value of the car after 3 years is $3375.

Let me know if you have any questions or want detailed steps for this calculation.

Expanding Questions:

1. How would the formula change if the depreciation rate varied each year?
2. What would be the value after 5 years instead of 3?
3. How can you calculate the original value if you know the final value and depreciation rate?
4. What happens to the value if the depreciation rate increases to 30%?
5. Can you graph the car's value over time with different depreciation rates?

Tip: To simplify exponential calculations, use a scientific calculator or computational tools like Excel or Python.