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+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+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?

The function e (x) shows the rate at which the coffee is added to the urn, x hours after it opened.

So, e (4) means the rate at which coffee is added to the urn after 4 hours of its opening which is 10 a. m.

The function I (x) shows the rate at which coffee is dispensed from the urn, x hours after it opened.

So, I (4) means the rate at which coffee is dispensed from the urn after 4 hours of its opening which is 10 a. m

(e - I) (x) = e (x) - I (x)

So, (e - I) (4) = e (4) - I (4) = 122 cups of coffee per hour

Thus, (e - I) (4) will represent the net rate at which coffee is added to the machine at 10 a. m. So we can conclude that 122 cups of coffee are added to the urn at 10 a. m