To determine which type of function best models the data in the table with points (1, 26), (4, 86), and (7, 146), we can analyze the pattern in the y-values as the x-values increase.
Calculating the differences:
- From (1, 26) to (4, 86): The change in y is \(86 - 26 = 60\) when x increases from 1 to 4 (an increase of 3 in x).
- From (4, 86) to (7, 146): The change in y is \(146 - 86 = 60\) when x increases from 4 to 7 (an increase of 3 in x again).
The consistent increase of 60 in y for each increase of 3 in x suggests a linear relationship, meaning the data can be modeled by a linear function of the form \(y = mx + b\).
In conclusion, the linear function best models this data because the rate of change in y remains constant as x increases.