An Application of Geometric Series to Medical Dosage.

A dosage of Q units of a certain drug is administered to an individual. Assume that, as the body eliminates the drug, the rate of decrease of concentration in the blood is proportional to the concentration itself.

(a) Explain why the amount of the drug in the bloodstream at the end of t hours is given by Qe^-ct where c is a positive constant.

(b)Suppose that the same dosage is given at successive T-hour intervals. Show that the amount A(N) of the drug in the bloodstream after the N'th dose is given by:

	N-1
A(N)=		Qe(-cT)n
	n=0

(c) Find an upper bound for the amount of drug in the bloodstream after any number of doses.

(d) Find the smallest time between doses that will ensure that A(N) does not exceed one half of a certain dangerous level D.