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The problem involves analyzing retail sales data for drug stores in the U.S., given as billions of dollars for years since 1995. The linear model provided is:

\[
F(t) = 9.44t + 84.182
\]
where $ t $ represents the number of years since 1995, and $ F(t) $ gives the predicted retail sales in billions of dollars.

### 1. Scatter Plot Analysis
The scatter plot shows data points alongside the linear model. It appears the data points are very close to the line, which suggests the linear model fits the data well.

So, based on the scatter plot, the answer to the first question is:
- **The function is a good model for the data**.

### 2. Estimating Retail Sales in 2014
To estimate retail sales in 2014, we calculate $ t = 2014 - 1995 = 19 $ years. Plugging $ t = 19 $ into the linear model:

\[
F(19) = 9.44(19) + 84.182 = 179.36 + 84.182 = 263.542 \text{ billion dollars}.
\]

Therefore, the estimated retail sales in 2014 would be **263.54 billion dollars**.

### 3. Predicting the Year for $231 Billion in Sales
To predict when retail sales will reach $231 billion, set $ F(t) = 231 $ and solve for $ t $:

\[
231 = 9.44t + 84.182
\]
\[
231 - 84.182 = 9.44t
\]
\[
146.818 = 9.44t
\]
\[
t = \frac{146.818}{9.44} \approx 15.56
\]

Since $ t $ is approximately 15.56, this corresponds to **1995 + 15.56 = 2010.56**. So, sales will reach $231 billion around mid-2011.

---

Let me know if you want further details on these calculations. Here are some additional related questions:

1. How would the model change if the rate of sales growth increased?
2. What would the sales be predicted in the year 2025 using this model?
3. Can the linear model be used to predict sales indefinitely?
4. How could we adjust the model to account for non-linear growth?
5. What would the year be for a sales target of $300 billion using this same model?

**Tip:** Linear models are great for short-term predictions, but for long-term trends, it's often better to check if other factors might affect the growth rate!

The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995. A linear model for the data is given as F(t) = 9.44t + 84.182, where t represents the number of years since 1995. Use the model to estimate the retail sales in the U.S. in 2014, and predict the year in which retail sales will be $231 billion.

Learn how to estimate retail sales in drug stores using a linear model F(t) = 9.44t + 84.182. This problem helps you understand how to predict sales for a specific year, such as 2014, and how to use algebra to determine when sales will reach $231 billion. Suitable for students in Grades 10-12.

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