Question

Which type of function best models the data in the table?

Type of Function

x y
1
1
10
10

2
2
100
100

3
3
1000
1000

4
4
10000
10000



(1 point)
Responses

cubic
cubic

linear
linear

exponential
exponential

quadratic

Answer 1

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

```
x | y
-------------
1 | 10
2 | 100
3 | 1000
4 | 10000
```

If we look at the values of \( y \):

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

We can see that \( y \) increases by a factor of 10 as \( x \) increases by 1:

- From \( 10 \) (when \( x = 1 \)) to \( 100 \) (when \( x = 2 \)) is a factor of 10.
- From \( 100 \) (when \( x = 2 \)) to \( 1000 \) (when \( x = 3 \)) is also a factor of 10.
- From \( 1000 \) (when \( x = 3 \)) to \( 10000 \) (when \( x = 4 \)) is again a factor of 10.

This pattern indicates that the relationship between \( x \) and \( y \) is exponential. Specifically, the equation \( y = 10^{x} \) seems to fit the data.

Therefore, the type of function that best models the data in the table is:

**exponential.**