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Question

Find the rate of change for the table below
Input Output
2 6
7 21
9 27
11 33

3

4

1

5

Answer 1

To find the rate of change in the table provided, we need to calculate the change in output divided by the change in input between each pair of successive points.

The points from the table are:

1. (2, 6)
2. (7, 21)
3. (9, 27)
4. (11, 33)

Now, let’s calculate the rate of change between each pair of points:

1. Between (2, 6) and (7, 21): $$\text{Rate of change}=\frac{21-6}{7-2}=\frac{15}{5}=3$$

2. Between (7, 21) and (9, 27): $$\text{Rate of change}=\frac{27-21}{9-7}=\frac{6}{2}=3$$

3. Between (9, 27) and (11, 33): $$\text{Rate of change}=\frac{33-27}{11-9}=\frac{6}{2}=3$$

The rate of change between each pair of points in the table is consistent, and it is equal to 3.

Thus, the rate of change is 3 for each interval.