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.
(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=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.
If your browser does not support superscripts, the formula in (b) is available also in jpg format