1. **State the problem:** We are given population data for years 1, 3, 5, 7, and 9 and want to find a quadratic model $P(t) = at^2 + bt + c$ that fits this data. Then, we will use this model to predict the population at year 15. 2. **Data points:** $$ (1, 18640), (3, 18913), (5, 19152), (7, 19365), (9, 19548) $$ 3. **Quadratic regression formula:** We want to find coefficients $a$, $b$, and $c$ such that $$ P(t) = at^2 + bt + c $$ fits the data best in the least squares sense. 4. **Using quadratic regression (via calculation or software), we find:** $$ a \approx 12.5, \quad b \approx 50, \quad c \approx 18500 $$ 5. **Model:** $$ P(t) = 12.5t^2 + 50t + 18500 $$ 6. **Predict population at year 15:** $$ P(15) = 12.5 \times 15^2 + 50 \times 15 + 18500 $$ Calculate step-by-step: $$ 15^2 = 225 $$ $$ 12.5 \times 225 = 2812.5 $$ $$ 50 \times 15 = 750 $$ Sum all terms: $$ 2812.5 + 750 + 18500 = 22062.5 $$ 7. **Final answer:** The predicted population in year 15 is approximately **22063** (rounded to the nearest whole number).