https://file.aiquickdraw.com/mathbot/file/1726683857730wc8zq6r3.jpg

The image presents a scatterplot showing the change in hundreds of cookies baked at a bakery over eight days, with the x-axis labeled "Day" and the y-axis labeled "Change in Hundreds of Cookies from Previous Day." Below the graph, a scenario is described where the number of cookies baked changes based on demand. Specifically, the point at (2, 5) indicates that on day 2, 500 more cookies were baked than on day 1.

The question asks which statement supports the selection of a model for \( C \), where \( C \) is a function representing the number of cookies baked on each day.

### Observations:
- The graph shows the rate of change in the number of cookies baked each day.
- At first, there is an increase (positive values) in the number of cookies, followed by a decrease (negative values) in the later days.
- The graph suggests the changes are not completely linear but follow a trend that starts high and gradually decreases.

The statement in **option A** is:  
- *Because the information about rate of change is roughly linear, a linear model is best for \( C \).*

This option supports selecting a linear model for the function \( C \), despite the changes in the rate of cookie production not being perfectly linear. The general trend could be described with a linear model, especially considering the gradual decrease in production rate after a certain point.

### Key takeaway:
Although the points are not strictly linear, the trend follows a pattern that might approximate a linear relationship, which is why option A suggests a linear model for \( C \).

Would you like a detailed explanation of why linear models are suggested for approximate trends? Let me know if you have any questions!

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Here are five related questions:
1. How can a linear model approximate trends even with non-linear data?
2. What are the characteristics of a linear model?
3. How can we determine if a different model, like a quadratic one, fits better?
4. Why do we use scatterplots to visualize changes over time in real-world data?
5. What would happen if the points on the graph showed a strong curvature rather than a trend?

**Tip**: When deciding on a model for data, look at the overall trend rather than expecting a perfect fit with every point.

At a bakery, the number of cookies baked each day changes based on anticipated demand. The scatterplot shows the change in hundreds of cookies baked from the previous day for eight days. The point at (2, 5) means that on day 2, the number of cookies baked will be 500 more than on day 1. A function model C is to be constructed for the number of cookies baked on each of the days, 0 through 8. Which of the following statements best supports the selection of a model for C?

Analyze the rate of change in cookie production at a bakery over eight days. The scatterplot indicates an increasing and then decreasing trend in hundreds of cookies baked per day. Understand how to select a linear model for the number of cookies baked each day, with a focus on data trend analysis. Suitable for students in Grades 9-12.

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