Question

Compute the maximum and minimum amount of a drug remaining in a patient
in the limit (that is, as time tends to infinity) given that the patient takes an 80 milligram dose
once a day at the same time each day and the drug has a half life of 22 hours.

Answer 1

starting at time 0, when the first dose is taken, the amount after t hours is

80*(1/2)^(t/22)
the 2nd dose:
80*(1/2)^((t-24)/22)
the nth dose:
80*(1/2)^((t-24n)/22)

Play around with that as t gets large.