Question

17. Two tables of data are shown.
sample A sample B
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
Sample B changes by a common
When x = 4, both y values will be

Answer 1

To analyze the two samples, we need to determine how Y changes in relation to X in each sample.

1. **Sample A changes by a common**: factor of 2. Looking at the Y values:
- When X = 0, Y = 2
- When X = 1, Y = 4 (change of 2)
- When X = 2, Y = 8 (change of 4)
- When X = 3, Y = 16 (change of 8)

The pattern shows that as X increases by 1, the Y values are influenced by the previous Y value, effectively multiplying.

However, the exact relation can be seen: \(Y \text{(Sample A)} = 2^X\).

2. **Sample B changes by a common**: factor of 6. Looking at the Y values:
- When X = 0, Y = 8
- When X = 1, Y = 14 (change of 6)
- When X = 2, Y = 20 (change of 6)
- When X = 3, Y = 26 (change of 6)

The Y values increase by a constant amount of 6 as X increases by 1.

Thus, it shows a linear relationship: \(Y \text{(Sample B)} = 6X + 8\).

3. **When x = 4, both y values will be**:
- For Sample A:
\[
Y = 2^X \implies Y = 2^4 = 16
\]
- For Sample B:
\[
Y = 6X + 8 \implies Y = 6(4) + 8 = 24 + 8 = 32
\]

So, the complete statements are:
- Sample A changes by a common **factor of 2 (exponential)**.
- Sample B changes by a common **factor of 6 (linear)**.
- When X = 4, both Y values will be **16 (Sample A) and 32 (Sample B)**.