Let's break down the problem step by step:

1. Linear Model Interpretation: The given linear equation is $y = -0.34x + 25.34$, where $x$ represents the person's age and $y$ represents the time spent on the internet in hours per week.

2. Why was a linear function chosen?:

   • The selected option is correct: "A linear function was chosen because the time decreases by approximately the same amount for each increase in age." This is evident from the table, where the hours spent on the internet decreases fairly uniformly as age increases.

3. Prediction for a 49-year-old:

   • The model predicts the time using the formula $y = -0.34x + 25.34$.
   • For $x = 49$: $y = -0.34(49) + 25.34 = -16.66 + 25.34 = 8.68$
   • Rounded to the nearest tenth, the prediction is 8.7 hours.

4. Comparison of predicted vs actual time for a 49-year-old:

   • The table shows that a 49-year-old spends 6 hours on the internet.
   • The predicted value from the model is 8.7 hours, which is more than the actual value.
   • To find the difference: $8.7 - 6 = 2.7$
   • Therefore, the model overestimates the time by 2.7 hours.

Let me know if you'd like any further details or clarifications!

Here are 5 related questions to deepen your understanding:

1. What does the slope of -0.34 in the linear model represent in terms of time spent on the internet?
2. How would the model change if the time spent increased with age instead of decreasing?
3. What are some limitations of using a linear model to predict behavior like internet usage over time?
4. Can you think of other factors besides age that might affect the amount of time spent on the internet?
5. How would the prediction for a 72-year-old compare to the actual data?

Tip: When interpreting linear models, always check the slope. It indicates the rate of change between the variables, helping you understand the direction and magnitude of the trend.