Many drugs are eliminated from the body in an exponential manner. Thus, if a drug is given in dosages of size C at time intervals of length t, the amount An of the drug in the body just after the (n + 1)st dose is
An = C + Ce-kt + .... + Ce-nkt
Where k is a positive constant that depends on the type of drug.
(a) Derive a formula for A, the amount of drug in the body just after a dose, if a person has been on the drug for a very long time (assume an infinitely long time).
(b) Evaluate A if it is known that one-half of a dose is eliminated from the body in 6 hours and doses of size 2 milligrams are given every 12 hours.