Question

The table represents the heights of a plant recorded occasionally over weeks.
week height (in inches)
4 24
6 27
8 30
12 48

What is the average rate of change of the height of the plant between Week and Week ?

Responses

inches per week
3 inches per week

inches per week
4 inches per week

inches per week

Answer 1

To find the average rate of change of the height of the plant between two specific weeks, we can use the formula:

\[
\text{Average Rate of Change} = \frac{\text{Change in Height}}{\text{Change in Time}} = \frac{h_2 - h_1}{t_2 - t_1}
\]

where \(h_1\) and \(h_2\) are the heights at time \(t_1\) and \(t_2\) respectively.

Let's clarify which two weeks you want to calculate the average rate of change for. If you want to calculate it between Week 4 and Week 12, the heights are as follows:

- At Week 4, height = 24 inches (h_1)
- At Week 12, height = 48 inches (h_2)

Now substituting these values into our formula:

\[
\text{Average Rate of Change} = \frac{48 - 24}{12 - 4}
\]

Calculating the difference in heights and the difference in weeks:

\[
= \frac{24}{8} = 3 \text{ inches per week}
\]

Therefore, the average rate of change of the height of the plant between Week 4 and Week 12 is **3 inches per week**.

If you're looking for the average rate of change between different weeks, please specify which weeks you would like to calculate.