1. **State the problem:** We have a car purchased for 20700 dollars, and its value depreciates by 11% per year. We want to find the value of the car after 11 years. 2. **Formula used:** The formula for depreciation is: $$ V = P(1 - r)^t $$ where: - $V$ is the value after $t$ years, - $P$ is the initial value, - $r$ is the depreciation rate (as a decimal), - $t$ is the number of years. 3. **Identify values:** - $P = 20700$ - $r = 0.11$ - $t = 11$ 4. **Calculate:** $$ V = 20700(1 - 0.11)^{11} = 20700(0.89)^{11} $$ 5. **Evaluate the power:** Calculate $0.89^{11}$: $$ 0.89^{11} \approx 0.2759 $$ 6. **Multiply:** $$ V = 20700 \times 0.2759 = 5700.13 $$ 7. **Final answer:** The value of the car after 11 years is approximately **5700.13 dollars**.