1. **State the problem:** Felicia buys a motorcycle for 3985. Each year its value depreciates by $x\%$. After 7 years, its value is 3269. We need to find $x$ to 2 decimal places. 2. **Formula used:** The value after depreciation each year is given by the formula for exponential decay: $$ V = P \times \left(1 - \frac{x}{100}\right)^t $$ where $V$ is the value after $t$ years, $P$ is the initial value, and $x$ is the depreciation rate percentage. 3. **Substitute known values:** $$ 3269 = 3985 \times \left(1 - \frac{x}{100}\right)^7 $$ 4. **Isolate the decay factor:** $$ \left(1 - \frac{x}{100}\right)^7 = \frac{3269}{3985} $$ 5. **Calculate the right side:** $$ \frac{3269}{3985} \approx 0.8201 $$ 6. **Take the 7th root of both sides:** $$ 1 - \frac{x}{100} = \sqrt[7]{0.8201} $$ 7. **Calculate the 7th root:** $$ \sqrt[7]{0.8201} \approx 0.9736 $$ 8. **Solve for $x$:** $$ 1 - \frac{x}{100} = 0.9736 $$ $$ \frac{x}{100} = 1 - 0.9736 = 0.0264 $$ 9. **Convert to percentage:** $$ x = 0.0264 \times 100 = 2.64\% $$ **Final answer:** The annual depreciation rate is **2.64\%**.