To correct the answers based on the information provided, let's analyze the problem step by step.

Given Information:

1. The linear model for retail sales is $F(t) = 9.44t + 84.182$, where $t$ is the number of years since 1995.
2. You need to:
   • Estimate retail sales in the U.S. for 2014.
   • Predict the year when retail sales will reach $246 billion.

Step 1: Retail Sales in 2014

• 2014 corresponds to $t = 2014 - 1995 = 19$.
• Substitute $t = 19$ into $F(t)$: $F(19) = 9.44(19) + 84.182$ $F(19) = 179.36 + 84.182 = 263.542$

Thus, the retail sales in 2014 are $263.542 billion, which is correct.

Step 2: Year When Retail Sales Reach $246 Billion

• Set $F(t) = 246$ and solve for $t$: $246 = 9.44t + 84.182$ Subtract 84.182 from both sides: $246 - 84.182 = 9.44t$ $161.818 = 9.44t$ Divide both sides by 9.44: $t = \frac{161.818}{9.44} \approx 17.15$

• The year is $1995 + 17.15 \approx 2012$.

Thus, retail sales will reach $246 billion in 2012, which is correct.

Conclusion:

• Retail sales in 2014: $263.542 billion.
• Year for $246 billion: 2012.

Both values are correct based on the given model.

If you entered these incorrectly before, double-check your input format in the platform. Let me know if further clarification is needed!

5 Follow-Up Questions:

1. Can you derive $t$ for any other retail sales value using the given formula?
2. How would the predictions change if the slope (9.44) increased or decreased?
3. What assumptions are inherent in using a linear model for these data?
4. How does the scatter plot help verify the model's accuracy?
5. Could a quadratic or exponential model better fit the data?

Tip:

Always recheck whether $t$ refers to the correct year offset from 1995 to avoid calculation mistakes!