Question

Which of the following best models the data in the table?

Type of Function

x y
2
2
8.5
8.5
4
4
46
46
6
6
107.5
107.5
8
8
193
193
(1 point)
Responses

exponential
exponential

linear
linear

quadratic
quadratic

cubic

Answer 1

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.

1. For a **linear function**, we would expect y to change at a constant rate as x changes.
2. For a **quadratic function**, y would change at a rate that is not constant but is smooth—essentially, the second differences would be constant.
3. For a **cubic function**, the rate of change in y would involve more complexity than in quadratic functions.
4. 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**.