https://file.aiquickdraw.com/mathbot/file/1728360024451exv7kcjh.jpg

The problem shown in the image asks:

"A vehicle purchased for $32,500 depreciates at a constant rate of 4%. Determine the approximate value of the vehicle 12 years after purchase. Round to the nearest whole dollar."

This is an exponential depreciation problem. The formula for exponential depreciation is:

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

Where:
- $ V $ is the value after depreciation,
- $ P $ is the initial value (in this case, $32,500),
- $ r $ is the rate of depreciation (4% or 0.04),
- $ t $ is the time in years (12 years here).

### Step-by-step Calculation:
1. **Initial Value (P):** $32,500
2. **Depreciation Rate (r):** 4% or 0.04
3. **Time (t):** 12 years

\[
V = 32500 \times (1 - 0.04)^{12}
\]
\[
V = 32500 \times (0.96)^{12}
\]
\[
V \approx 32500 \times 0.6246 \quad (\text{using a calculator for } (0.96)^{12})
\]
\[
V \approx 20200.52
\]

### Final Answer:
The approximate value of the vehicle after 12 years is **$20,201** (rounded to the nearest whole dollar).

Would you like more details or have any questions?

Here are some related questions to explore:
1. What is the formula for depreciation when the rate changes every year?
2. How would the value change if the depreciation rate was 6% instead of 4%?
3. How is exponential depreciation different from linear depreciation?
4. What would be the value of the car after 15 years at 4% depreciation?
5. How can you calculate depreciation for assets that appreciate in value?

**Tip:** Always remember to express percentages in decimal form when applying them in formulas (e.g., 4% = 0.04).

A vehicle purchased for $32,500 depreciates at a constant rate of 4%. Determine the approximate value of the vehicle 12 years after purchase. Round to the nearest whole dollar.

Learn how to calculate the depreciation of a vehicle purchased for $32,500 at a 4% constant rate over 12 years. This problem uses the exponential depreciation formula, and the final vehicle value is approximately $20,201. Suitable for high school students and beyond.

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