1. **State the problem:** We want to find the value of a car after 5 years, given it depreciates at 5.75% per year from an initial value of 16500. 2. **Formula used:** The value after $t$ years with annual depreciation rate $r$ is given by the exponential decay formula: $$ V = P(1 - r)^t $$ where: - $P$ is the initial value, - $r$ is the depreciation rate as a decimal, - $t$ is the number of years, - $V$ is the value after $t$ years. 3. **Identify values:** - $P = 16500$ - $r = 5.75\% = 0.0575$ - $t = 5$ 4. **Calculate:** $$ V = 16500(1 - 0.0575)^5 = 16500(0.9425)^5 $$ 5. **Evaluate the power:** $$ (0.9425)^5 \approx 0.7423 $$ 6. **Multiply:** $$ V = 16500 \times 0.7423 = 12248.04 $$ 7. **Final answer:** The value of the car after 5 years is approximately **12248.04** dollars.