To determine which type of function models the provided data, we need to analyze the relationship between the x and y values.
The data is as follows:
| x | y | |----|------| | 2 | 2 | | 4 | 4 | | 8 | 8 | | 46 | 46 | | 6 | 6 | | 107.5 | 107.5 | | 8 | 8 | | 193 | 193 |
Looking at the data, x appears to take on specific values, and the corresponding y values seem to follow a pattern. There are intervals where there might be consistent increases, but we have to identify if this pattern is linear, quadratic, or something else, such as exponential.
- For a linear function, we would expect y to change at a constant rate as x changes.
- For a quadratic function, y would change at a rate that is not constant but is smooth—essentially, the second differences would be constant.
- For a cubic function, the rate of change in y would involve more complexity than in quadratic functions.
- An exponential function would show increasingly rapid changes.
To see which type it fits best, we could calculate the differences between y values, but since the numbers are not well-aligned in increments, we can consider another approach: plotting or checking if y is a multiple of x in a specific way.
However, based on the highlighting of ranges and by looking at the dramatic increase in values between inputs, the exponential function seems to show a pronounced increase as x increases.
Thus, the best-fit model for the data in the table appears to be exponential.
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