Question

17. Two tables of data are shown.
x y x y
0 2 0 8
1 4 1 14
2 8 2 20
3 16 3 26



(3 points)
Complete the statements below:

Sample A changes by a common
factor
Sample B changes by a common
factor
When x = 4, both y values will be
32
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Answer 1

To analyze the two samples given:

**Sample A:**
- The observations are:
- (0, 2)
- (1, 4)
- (2, 8)
- (3, 16)

You can see how the values of \(y\) change:
- From 2 to 4 (increased by 2)
- From 4 to 8 (increased by 4)
- From 8 to 16 (increased by 8)

This shows that each change in \(y\) doubles the previous change. Hence, sample A changes by a common **factor of 2**.

**Sample B:**
- The observations are:
- (0, 8)
- (1, 14)
- (2, 20)
- (3, 26)

You can see how the values of \(y\) change:
- From 8 to 14 (increased by 6)
- From 14 to 20 (increased by 6)
- From 20 to 26 (increased by 6)

This consistent change indicates that each change in \(y\) is **by a common factor of 6**.

**Completion of Statements:**

Sample A changes by a common **factor of 2**.
Sample B changes by a common **factor of 6**.
When \(x = 4\), both \(y\) values will be **32**.

This is indicated by:
- For Sample A, if you continue to double (16 * 2) the \(y\) value, you will indeed get \(32\).
- For Sample B, similarly, the linear pattern shows that \(y\) continues increasing by 6. Thus, \(26 + 6 = 32\).