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

linear
linear

quadratic
quadratic

cubic
cubic

exponential

Answer 1

To determine the type of function that best models the given data, we need to analyze the relationship between \( x \) and \( y \):

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

We can observe that each corresponding \( y \) value is increasing by a factor of 10 as \( x \) increases by 1:

- \( y \) increases from \( 10 \) to \( 100 \) (factor of 10)
- \( y \) increases from \( 100 \) to \( 1000 \) (factor of 10)
- \( y \) increases from \( 1000 \) to \( 10000 \) (factor of 10)

This pattern suggests that the relationship is exponential. An exponential function has the form \( y = ab^x \), where \( b \) is the base of the exponential growth.

Based on this analysis, the type of function that best models the data is:

**Exponential**.