The rate of change of the height of the water in the tank can be found by calculating the slope between any two points on the table. Therefore, the rate of change in the height of the water in the tank is 2 feet per minute.
The rate of change of the height of the water in the tank with respect to time can be found by calculating the slope of the line connecting any two points on the table. The formula for calculating slope is given by:
slope = (change in height)/(change in time)
For example, to find the rate of change between time 0 and time 1, we subtract the initial height from the final height and divide it by the difference in time:
(35 - 32.5)/(1 - 0)
= 2.5 feet per minute.
Similarly, the rate of change between time 7 and time 13 can be calculated as:
(17.5 - 2.5)/(13 - 7)
= 2 feet per minute.