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

Cubic
Cubic

Quadratic
Quadratic

Exponential

Answer 1

To determine the type of function that best models the data in the table, let's analyze the values:

- As \( x \) increases from 1 to 4, the values of \( y \) increase dramatically:
- \( y(1) = 10 \)
- \( y(2) = 100 \)
- \( y(3) = 1000 \)
- \( y(4) = 10000 \)

Examining the pattern:
- \( 10 \) (for \( x = 1 \)) is \( 10^1 \)
- \( 100 \) (for \( x = 2 \)) is \( 10^2 \)
- \( 1000 \) (for \( x = 3 \)) is \( 10^3 \)
- \( 10000 \) (for \( x = 4 \)) is \( 10^4 \)

This suggests an exponential growth factor where \( y = 10^x \).

Therefore, the type of function that best models the data is **Exponential**.