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

exponential
exponential

quadratic
quadratic

cubic
cubic

Answer 1

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

The data provided is:

\[
\begin{align*}
x & : 1, 2, 3, 4 \\
y & : 10, 100, 1000, 10000 \\
\end{align*}
\]

Observing the \( y \) values, we can see that they increase by a factor of 10 as \( x \) increases by 1:

- 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 consistent multiplicative increase suggests that the relationship between \( x \) and \( y \) is exponential in nature, specifically in the form of \( y = 10^x \).

Thus, the best model for the data is:

**Exponential**