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The table shows the relationship between the number of years since the account was opened, \(x\), and the money in the account, \(f(x)\).

To complete the question:

1. **Function Type**: Based on the increasing pattern in the data, the growth appears to be linear because the money increases by approximately the same amount each year. Therefore, a **linear function** would likely model the data better.

2. **y-values Change**: As \(x\) increases, the \(y\) values increase at a **constant rate**. To check, calculate the difference in \(f(x)\) for each increase in \(x\):
   - From \(x=1\) to \(x=2\), \( \Delta y = 432.13 - 222.13 = 210 \)
   - From \(x=2\) to \(x=3\), \( \Delta y = 643.18 - 432.13 = 211.05 \)
   - From \(x=3\) to \(x=4\), \( \Delta y = 853.81 - 643.18 = 210.63 \)
   
   These values are very close to each other, confirming that the increase is roughly constant.

3. **Slope**: The rate of change (slope) of the function is approximately **210** (or slightly above 210, based on the differences calculated).

Thus, the missing parts of the answer can be filled as follows:
- A **linear** function would better model the data because as \(x\) increases, the \(y\) values change by a **constant rate**. 
- The **slope** of this function is approximately **210**.

Would you like further clarification or details?

Here are 5 follow-up questions to deepen understanding:
1. How would you graph this linear model based on the data points?
2. What would the equation of the linear function be using slope-intercept form?
3. Could any other type of function (quadratic, exponential) fit the data, and why or why not?
4. How does the concept of slope relate to real-world applications, such as in this banking context?
5. If this pattern continued, how much money would be in the account after 5 or 6 years?

**Tip**: When dealing with real-world data, checking for constant differences (for linear models) or ratios (for exponential models) can help identify the type of function that best fits the data.

A function would better model the data because as x increases, the y values change at a constant rate. The slope of this function is approximately 210.

Learn how to model a linear function using data where the money in an account increases by a constant rate each year. This problem involves calculating the slope and understanding the linear relationship between the number of years and the money in the account. Suitable for students in Grades 8-10.

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