1. **State the problem:** A city doubles its population every 83 years. The current population is 88,200. We want to find the population after 249 years. 2. **Formula used:** The population growth can be modeled by the exponential growth formula: $$ P(t) = P_0 \times 2^{\frac{t}{T}} $$ where: - $P(t)$ is the population at time $t$, - $P_0$ is the initial population, - $T$ is the doubling time (83 years), - $t$ is the time elapsed (249 years). 3. **Substitute the known values:** $$ P(249) = 88200 \times 2^{\frac{249}{83}} $$ 4. **Calculate the exponent:** $$ \frac{249}{83} = 3 $$ 5. **Evaluate the power of 2:** $$ 2^3 = 8 $$ 6. **Calculate the final population:** $$ P(249) = 88200 \times 8 = 705600 $$ 7. **Answer:** The population after 249 years will be **705,600** people.