To determine the type of function that best models the data in the given table, we can analyze the changes between the values of \( y \) corresponding to the values of \( x \):
- For \( x = 1 \): \( y = 26 \)
- For \( x = 4 \): \( y = 86 \)
- For \( x = 7 \): \( y = 146 \)
Calculating the differences:
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The difference from \( x = 1 \) to \( x = 4 \):
- \( 86 - 26 = 60 \)
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The difference from \( x = 4 \) to \( x = 7 \):
- \( 146 - 86 = 60 \)
Now, let's look at these differences:
- The differences between \( y \) values are the same from \( x = 1 \) to \( x = 4 \) and from \( x = 4 \) to \( x = 7 \):
- First difference: \( 60 \)
- Second difference is not constant.
To further evaluate if the function is quadratic, we would calculate the second differences. However, since the first differences are not changing, it suggests a linear relationship.
The consistent addition suggests that this dataset appears to follow a linear model because the change in \( y \) for equally spaced changes in \( x \) is constant (or similar).
Thus, the best model for the data is:
Linear
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