To solve part C, you need to use the linear model given:

$y = 9.44x + 84.182$

where:

• $y$ represents the retail sales in billions of dollars.
• $x$ represents the years since 2000.

You are asked to predict the year when retail sales will reach $253 billion. This means setting $y = 253$ and solving for $x$.

Steps:

1. Substitute $y = 253$ into the equation: $253 = 9.44x + 84.182$

2. Rearrange to solve for $x$: $9.44x = 253 - 84.182$ $9.44x = 168.818$ $x = \frac{168.818}{9.44}$ $x \approx 17.88$

3. Since $x$ represents years since 2000, add 2000 to this value: $2000 + 17.88 \approx 2017.88$

Answer:

The model predicts that retail sales will reach $253 billion around the year 2018.

Would you like more details on any steps?

1. What is the importance of the slope in a linear model?
2. How do we interpret the y-intercept in this context?
3. How would this model change if the growth rate were different?
4. What if the target value were different—how would that impact our solution?
5. How could you verify if this model continues to be accurate over time?

Tip: Always recheck your calculations when using models to predict future values, especially with real-world data.