Question

A large coffee urn dispenses coffee at a hospital cafeteria.The cafeteria is open from 6 am until 7 pm daily. The rate at which coffee is added to the urn is modeled by the function e(x)=3x3+20e(x)=3x3+20 , where the rate is measured in cups of coffee per hour since the cafeteria opened. The rate at which coffee is dispensed from the urn is modeled by the function l(x)=5x2+10l(x)=5x2+10 , where the rate is measured in cups of coffee per hour since the cafeteria opened. What does (e−l)(4) mean in this situation?
A. There are 302 cups of coffee in the urn 4 hours after the cafeteria opened.
B. The rate at which the number of cups of coffee in the urn is changing 4 hours after the cafeteria opened is 302 cups per hour.
C.
There are 122 cups of coffee in the urn 4 hours after the cafeteria opened.
D. The rate at which the number of cups of coffee in the urn is changing 4 hours after the cafeteria opened is 122 cups per hour.

Answer 1

Think:  Coffee is entering the urn at the same time that coffee is being withdrawn from the urn.  Generally the former rate is greater than the latter, 'tho this is not always the case.  (e - l)(t) signifies the NET amount of coffee in the urn.  If e - l is decreasing, then the amount of coffee there is decreasing.  If e - l is increasing, then the amount of coffee in the urn is increasing, and the urn could eventually overflow.  Please use this info to select the correct answer.