Question

Two tables of data are shown.
x y
0 2
1 4
2 8
3 16
(3 points)
Complete the statements below:

Sample A changes by a common x y

Sample B changes by a common
When x = 4, both y values will be
x y
0 8
1 14
2 20Complete the statements below:

Sample A changes by a common
difference
Sample B changes by a common
factor
When x = 4, both y values will be
3 26

Answer 1

To analyze the data you provided and complete the statements, let's break down each sample:

### Sample A:
The data is as follows:
```
x y
0 2
1 4
2 8
3 16
```
- From \( x = 0 \) to \( x = 1 \): \( y \) changes from 2 to 4 (change of 2).
- From \( x = 1 \) to \( x = 2 \): \( y \) changes from 4 to 8 (change of 4).
- From \( x = 2 \) to \( x = 3 \): \( y \) changes from 8 to 16 (change of 8).

The y values are doubled for each increase of 1 in x, which suggests that the change in y is by a common **factor** of 2.

### Sample B:
The data is as follows:
```
x y
0 8
1 14
2 20
```
- From \( x = 0 \) to \( x = 1 \): \( y \) changes from 8 to 14 (change of 6).
- From \( x = 1 \) to \( x = 2 \): \( y \) changes from 14 to 20 (change of 6).

In this case, the y values increase by the same amount of 6 for each increase of 1 in x, which suggests that the change in y is by a common **difference** of 6.

### So the completed statements are:
- Sample A changes by a common **factor**.
- Sample B changes by a common **difference**.
- When x = 4, both y values will be **26** (from Sample B, as \( 20 + 6 = 26 \)).

For Sample A, substituting \( x = 4 \) yields \( y = 16 \times 2 = 32 \), and thus yields \( y = 32 \).

Therefore, we summarize:
1. Sample A changes by a common **factor**.
2. Sample B changes by a common **difference**.
3. When \( x = 4 \), both y values will be **32** (Sample A) and **26** (Sample B).