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

exponential
exponential

quadratic
quadratic

linear
linear

cubic

Answer 1

To determine which type of function best models the given data, let's first look at the values provided:

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

Now, let's examine the relationship between 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, \(y\) is multiplied by 10. This indicates a pattern consistent with an exponential function, specifically of the form \(y = a \cdot b^x\) where \(b\) is a positive constant.

If we assume \(y = 10^x\), we can see:
- For \(x = 1\), \(y = 10^1 = 10\)
- For \(x = 2\), \(y = 10^2 = 100\)
- For \(x = 3\), \(y = 10^3 = 1000\)
- For \(x = 4\), \(y = 10^4 = 10000\)

Every result matches the given values of \(y\).

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