Question

Which type of function best models the data in the table?
x y
1 10
2 100
3 1000
4 10000


(1 point)
Responses

Linear
Linear

Cubic
Cubic

Quadratic
Quadratic

Exponential
Exponential

Answer 1

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

The data points are:
- At \(x = 1\), \(y = 10\)
- At \(x = 2\), \(y = 100\)
- At \(x = 3\), \(y = 1000\)
- At \(x = 4\), \(y = 10000\)

Looking at the values of \(y\):
- When \(x\) increases from 1 to 2, \(y\) increases by a factor of 10 (from 10 to 100).
- When \(x\) increases from 2 to 3, \(y\) again increases by a factor of 10 (from 100 to 1000).
- When \(x\) increases from 3 to 4, \(y\) again increases by a factor of 10 (from 1000 to 10000).

This consistent multiplication of \(y\) by 10 for each increment in \(x\) indicates that the relationship is exponential, specifically \(y = 10^x\).

Therefore, the function that best models the data in the table is **Exponential**.