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

cubic
cubic

quadratic
quadratic

exponential
exponential

linear

Answer 1

To analyze the data in the table, we can look at the pairs of \(x\) and \(y\):

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

Notice that as \(x\) increases by 1, \(y\) increases by a factor of 10 each time. This suggests an exponential relationship, since the pattern can be represented as:

\[
y = 10^x
\]

Thus, the value of \(y\) grows exponentially with respect to \(x\).

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