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

quadratic
quadratic

exponential
exponential

cubic
cubic

linear

Answer 1

To determine which type of function best models the provided data, we can look at how the values of \(y\) change as \(x\) increases.

Here's the data you provided:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & 10 \\
2 & 100 \\
3 & 1000 \\
4 & 10000 \\
\hline
\end{array}
\]

**Observing the pattern:**
- From \(x = 1\) to \(x = 2\), \(y\) increases from 10 to 100 (a factor of 10).
- From \(x = 2\) to \(x = 3\), \(y\) increases from 100 to 1000 (another factor of 10).
- From \(x = 3\) to \(x = 4\), \(y\) increases from 1000 to 10000 (again a factor of 10).

The ratio of each successive \(y\) value is consistent (multiplied by 10), indicating that the relationship between \(x\) and \(y\) is exponential.

Given this pattern, the best fit for the function that models the data is:

**Exponential.**