1. **State the problem:** We need to find the population of a town after 5 years, given an initial population of 12,000 and an annual growth rate of 5%. 2. **Formula used:** The population growth can be modeled by the formula for exponential growth: $$P = P_0 (1 + r)^t$$ where: - $P$ is the population after $t$ years, - $P_0$ is the initial population, - $r$ is the growth rate (as a decimal), - $t$ is the number of years. 3. **Apply the values:** Initial population $P_0 = 12000$ Growth rate $r = 5\% = 0.05$ Time $t = 5$ years So, $$P = 12000 (1 + 0.05)^5 = 12000 (1.05)^5$$ 4. **Calculate $(1.05)^5$:** $$1.05^5 = 1.05 \times 1.05 \times 1.05 \times 1.05 \times 1.05 = 1.2762815625$$ 5. **Calculate the population:** $$P = 12000 \times 1.2762815625 = 15315.37875$$ 6. **Round to the nearest whole number:** $$P \approx 15315$$ **Final answer:** The population after 5 years will be approximately **15315** people.