John placed a container outside during a rainstorm.​A gauge on the side of the container shows the height, in millimeters, of the water in the container.

Question

​The table to the right lists the height of water the gauge showed along with the corresponding number of hours after the rainstorm started.

​What is the average rate of change, in millimeters per hour, of the ​height of water in the container from time 2 hours to 5 hours?

Answer 1

To find the average rate of change of the height of water in the container from 2 hours to 5 hours, we can use the formula for average rate of change, which is:

\[ \text{Average Rate of Change} = \frac{\text{Change in Height}}{\text{Change in Time}} \]

We need to know the height of the water at 2 hours and at 5 hours. If we assume the table provides those heights, let’s denote "height at 2 hours" as \( h(2) \) and "height at 5 hours" as \( h(5) \).

1. Find the heights:

   • Suppose \( h(2) = h_2 \) (the height of water at 2 hours)
   • Suppose \( h(5) = h_5 \) (the height of water at 5 hours)

2. Plug the values into the formula:

\[ \text{Average Rate of Change} = \frac{h(5) - h(2)}{5 - 2} \] \[ = \frac{h_5 - h_2}{3} \]

3. Calculate, once you have the values of \( h_2 \) and \( h_5 \).

Please provide the height values from the table if available, and we can continue with the calculations.