Question

Which type of function best models the data in the table?

Type of Function

x y
1
10
2
100
3
1000
4
10000


(1 point)
Responses

cubic
cubic

quadratic
quadratic

linear
linear

exponential

Answer 1

To determine the type of function that best models the given data, let's analyze the relationship between \(x\) and \(y\).

The table shows the following pairs:

- When \(x = 1\), \(y = 10\)
- When \(x = 2\), \(y = 100\)
- When \(x = 3\), \(y = 1000\)
- When \(x = 4\), \(y = 10000\)

We can observe that \(y\) increases significantly as \(x\) increases. Specifically, it appears that \(y\) is being multiplied by 10 for each increment in \(x\):

- From \(x = 1\) to \(x = 2\): \(10 \times 10 = 100\)
- From \(x = 2\) to \(x = 3\): \(100 \times 10 = 1000\)
- From \(x = 3\) to \(x = 4\): \(1000 \times 10 = 10000\)

This suggests an exponential growth pattern, where \(y\) can be described as a function of the form \(y = 10^x\).

Thus, the best model for this data is:

**Exponential**