Question 1200507


**Analysis:**

* **Visual Inspection:** By graphing the model and the scatterplot together, you can visually assess how well the model fits the data. 
    * If the curve of the function closely follows the trend of the scatterplot points, the model is considered a good fit.
    * If the curve significantly deviates from the data points, the model is not a good fit.

* **Glen Ellyn:** The model predicts that approximately 13.5% of police officers in Glen Ellyn are women.

* **Finding n when f(n) = 13:** 
    * The calculator provides two solutions: 108.7 and -408.7. 
    * Since population cannot be negative, the relevant solution is 108.7 thousand.
    * This means the model predicts that 13% of police officers are women in cities with populations of about 108.7 thousand.

**Based on visual inspection (which you would perform on your calculator), determine whether the model is a good fit for the data.**

**Key Points:**

* The model is an equation that attempts to describe the relationship between city population and the percentage of female police officers.
* The scatterplot helps visualize this relationship and assess how well the model captures the trend in the data.
* The model can be used to make predictions, such as estimating the percentage of female officers in a city with a given population.

I hope this helps! Let me know if you have any further questions.
**1. Graphing and Model Fit**

* **Using a graphing calculator:** 
    * Enter the data points (city population and percentage of female officers) into the lists. 
    * Graph the scatterplot of the data.
    * Enter the model equation (f(n) = 0.00006n^2 + 0.012n + 7.884) into the function editor.
    * Graph the model equation on the same graph as the scatterplot.

* **Visual Inspection:** 
    * Observe how closely the curve of the model fits the scatterplot points. 
    * If the curve closely follows the trend of the data points, the model is considered a good fit.

**2. Estimating Percentage of Female Officers in Glen Ellyn**

* **Substitute the population of Glen Ellyn (278.6 thousand) into the model equation:** 
    * f(278.6) = 0.00006 * (278.6)^2 + 0.012 * 278.6 + 7.884 
    * f(278.6) ≈ 13.5

* **The model estimates that approximately 13.5% of police officers in Glen Ellyn are women.**

**3. Finding n when f(n) = 13**

* **Set the model equation equal to 13:** 
    * 13 = 0.00006n^2 + 0.012n + 7.884

* **Solve for n:** 
    * This can be done using the quadratic formula or the "intersect" function on the graphing calculator. 
    * You should find two solutions for n: 
        * n ≈ 108.7 
        * n ≈ -408.7 

* **Interpretation:** 
    * The model predicts that 13% of police officers are women in cities with populations of about 108.7 thousand. 
    * The negative value (-408.7 thousand) is not meaningful in this context as population cannot be negative.

**Conclusion:**

* Based on the visual inspection of the graph, you can determine whether the model fits the data well. 
* The model can be used to estimate the percentage of female officers in cities with different populations.
* The interpretation of the results should consider the limitations of the model and the range of applicability of the data.

**Note:**

* This analysis assumes that the model is a reasonable representation of the relationship between city population and the percentage of female police officers. 
* Factors other than city population may also influence the percentage of female officers.

I hope this helps! Let me know if you have any other questions.