The table shows the amount of pet food in cups remaining in an automatic feeder as a function of the number of meals the feeder has dispensed.
Number of meals dispensed, n:1,3,6,7
Amount of pet food remaining, f (n) (cups):21,15,6,3
Based on the table, which value represents the rate of change
for this situation?
The rate of change in this situation can be found by calculating the difference in the amount of pet food remaining for consecutive meals.
For example, the rate of change from the 1st meal to the 3rd meal is:
f(3) - f(1) = 15 - 21 = -6 cups
Similarly, the rate of change from the 3rd meal to the 6th meal is:
f(6) - f(3) = 6 - 15 = -9 cups
Therefore, the value that represents the rate of change for this situation is -6 cups and -9 cups. It shows that the amount of pet food remaining in the feeder is decreasing at a rate of 6 cups and 9 cups per meal, respectively.