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The given problem asks for a quadratic regression model based on the population data and then requests the population prediction for year 18.

Here’s the process to solve it:

1. **Identify the data points:**
   - Year: [1, 4, 5, 8, 10]
   - Population: [16,559, 17,162, 17,339, 17,818, 18,094]

2. **Use Quadratic Regression:**
   We will fit the data points to a quadratic equation of the form:
   \[
   P(x) = ax^2 + bx + c
   \]
   where \( x \) is the year and \( P(x) \) is the population.

3. **Predict the population for year 18.**

I will calculate the regression equation and the population for year 18. Let me compute that for you.The quadratic regression model for the given data is:

\[
P(x) = -4.92x^2 + 224.40x + 16340.43
\]

Using this model, the predicted population for year 18 is approximately:

\[
P(18) \approx 18,785.84
\]

Would you like more details about the process or any specific part of this solution?

Here are some related questions for further exploration:
1. How would the model change if we used linear regression instead of quadratic?
2. What is the significance of the coefficients in the quadratic model?
3. How do we interpret the accuracy of this model based on the given data points?
4. Can this quadratic model be used to predict future years beyond 18?
5. What would the population be in year 15 using this same model?

**Tip:** When fitting a model, always verify it against actual data points to check its accuracy.

Determine a model for the given data by using quadratic regression. What will be the population in year 18?

Learn how to create a quadratic regression model to predict the population in year 18 based on provided data. This precalculus-level problem involves key algebraic concepts such as quadratic equations and data modeling. Data points include years 1, 4, 5, 8, and 10 with populations ranging from 16,559 to 18,094.

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