1. **State the problem:** Solve for the interest rate $r$ in the equation $$1000(1+r)^{10} = 2000.$$ 2. **Rewrite the equation:** Divide both sides by 1000 to isolate the exponential term: $$ (1+r)^{10} = \frac{2000}{1000} = 2.$$ 3. **Apply the 10th root:** To solve for $1+r$, take the 10th root of both sides: $$ 1+r = 2^{\frac{1}{10}}.$$ 4. **Calculate $r$:** Subtract 1 from both sides: $$ r = 2^{\frac{1}{10}} - 1.$$ 5. **Evaluate the expression:** Using a calculator or approximation, $$ 2^{0.1} \approx 1.0718,$$ so $$ r \approx 1.0718 - 1 = 0.0718.$$ **Final answer:** $$ r \approx 0.0718,$$ which means the interest rate is approximately 7.18%.