1. **State the problem:** We have a car purchased for 17900 dollars that depreciates at 12.25% per year. We want to find its value after 10 years. 2. **Formula used:** The value of an item depreciating exponentially is given by: $$ V = P(1 - r)^t $$ where: - $V$ is the value after $t$ years, - $P$ is the initial value, - $r$ is the depreciation rate (as a decimal), - $t$ is the time in years. 3. **Identify values:** - $P = 17900$ - $r = 0.1225$ - $t = 10$ 4. **Calculate:** $$ V = 17900(1 - 0.1225)^{10} $$ $$ V = 17900(0.8775)^{10} $$ 5. **Evaluate the power:** Calculate $0.8775^{10}$: $$ 0.8775^{10} \approx 0.2631 $$ 6. **Multiply:** $$ V = 17900 \times 0.2631 $$ $$ V \approx 4709.49 $$ 7. **Final answer:** The value of the car after 10 years is approximately **4709.49** dollars.