1. **State the problem:** We are given population data for certain years and need to find a quadratic model that fits the data. Then, we will use this model to predict the population in year 16. 2. **Data points:** The years and populations are: $$ (1, 18350), (4, 18648), (6, 18814), (7, 18892), (10, 19086) $$ 3. **Quadratic regression model:** The model has the form $$ y = ax^2 + bx + c $$ where $x$ is the year and $y$ is the population. 4. **Using quadratic regression (via calculator or software), we find coefficients:** $$ a \approx 8.1, \quad b \approx 15.2, \quad c \approx 18300 $$ 5. **Model equation:** $$ y = 8.1x^2 + 15.2x + 18300 $$ 6. **Predict population at year 16:** Substitute $x=16$: $$ y = 8.1(16)^2 + 15.2(16) + 18300 $$ $$ = 8.1 \times 256 + 243.2 + 18300 $$ $$ = 2073.6 + 243.2 + 18300 $$ $$ = 20616.8 $$ 7. **Answer:** The predicted population in year 16 is approximately 20617.