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The problem shown in the image involves depreciation using an exponential decay model. Let's break it down and solve it step by step.

### Problem:
A vehicle purchased for **$32,500** depreciates at a constant rate of **8% per year**. You are asked to find the approximate value of the vehicle **13 years** after purchase, rounded to the nearest whole number.

### Depreciation Formula:
The formula for exponential depreciation is:
\[
V(t) = P \cdot (1 - r)^t
\]
Where:
- $V(t)$ is the value after $t$ years,
- $P$ is the initial value (in this case, $32,500),
- $r$ is the rate of depreciation (8% or 0.08),
- $t$ is the time in years (13 years).

### Solution:
Let's plug in the values into the formula:
\[
V(13) = 32500 \cdot (1 - 0.08)^{13}
\]
\[
V(13) = 32500 \cdot (0.92)^{13}
\]
Now calculate $ (0.92)^{13} $.

\[
(0.92)^{13} \approx 0.377
\]
So,
\[
V(13) = 32500 \cdot 0.377 \approx 12253
\]

### Final Answer:
The approximate value of the vehicle after 13 years is **$12,253**, rounded to the nearest whole number.

Would you like a more detailed breakdown or have any other questions?

### Relative Questions:
1. How would the depreciation formula change if the rate were compounded monthly instead of yearly?
2. What is the value of the car after 20 years, using the same depreciation rate?
3. How would you calculate the time it takes for the car's value to depreciate to half its original price?
4. What would happen to the final value if the depreciation rate were 10% instead of 8%?
5. How does exponential depreciation differ from linear depreciation?

### Tip:
Always ensure to express the depreciation rate as a decimal in the formula by dividing the percentage by 100.

A vehicle purchased for $32,500 depreciates at a constant rate of 8%. Determine the approximate value of the vehicle 13 years after purchase, rounded to the nearest whole number.

Solve an exponential depreciation problem where a vehicle purchased for $32,500 depreciates at a constant rate of 8% per year. Find the approximate value after 13 years using the exponential decay formula. Suitable for high school students studying exponential functions.

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