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 20
3 26

Answer 1

To complete the statements about the two tables:

**Sample A changes by a common** **factor**.
The relationship in Sample A can be described as each y value is twice the previous y value.

**Sample B changes by a common** **increment**.
The relationship in Sample B can be described as each y value increases by a constant amount of 6 from the previous y value.

When **x = 4, both y values will be**:

- For Sample A:
Let's find the value of y when x = 4. Notice that in Sample A, \(y\) follows the pattern \(y = 2^x\). Thus, for \(x = 4\),
\(y = 2^4 = 16\).

- For Sample B:
The relationship in Sample B is linear, defined by \(y = 6x + 8\). Therefore, for \(x = 4\),
\(y = 6(4) + 8 = 24 + 8 = 32\).

So, when \(x = 4\), the values will be:

**Sample A:** \(y = 16\)
**Sample B:** \(y = 32\)