1. **Problem statement:** A bank account doubles every 5 years. We want to find the percent growth after 3 years, rounded to the nearest tenth of a percent. 2. **Formula and explanation:** If the account doubles every 5 years, the growth factor over 5 years is 2. We want the annual growth rate $r$ such that after 5 years the amount is doubled: $$ (1 + r)^5 = 2 $$ 3. **Find the annual growth rate $r$:** $$ 1 + r = \sqrt[5]{2} $$ $$ r = \sqrt[5]{2} - 1 $$ Calculate $r$: $$ r \approx 2^{0.2} - 1 \approx 1.1487 - 1 = 0.1487 $$ So the annual growth rate is approximately 14.87%. 4. **Calculate growth after 3 years:** The growth factor after 3 years is: $$ (1 + r)^3 = (1.1487)^3 $$ Calculate: $$ (1.1487)^3 \approx 1.1487 \times 1.1487 \times 1.1487 \approx 1.520 $$ 5. **Convert growth factor to percent growth:** Percent growth after 3 years is: $$ (1.520 - 1) \times 100\% = 0.520 \times 100\% = 52.0\% $$ **Final answer:** The bank account grows approximately 52.0% after 3 years.