Level of Medicine in the Human Body

Date: 11/1/96 at 19:12:28
From: brenchi
Subject: Level of Medicine in a Body

A hospital patient receives a 10mg dose of medicine at intervals of 
4 hours. During each interval, the amount of medicine in the patient's 
body reduces to 75 percent of the amount present at the beginning of 
the interval. Prove that there will always be less than 40mg of 
medicine present in the patient's body, regardless of the length of 
treatment.

I would really appreciate your help!

From Billy               

Date: 11/2/96 at 16:39:1
From: Doctor Anthony
Subject: Re: Level of Medicine in a Body

The amount of medicine present in the patient's body after an 
infinite amount of time is given by the sum of the series:

 10(1 + .75 + .75^2 + .75^3 + ... to infinity)

  = 10(1/(1-.75)  = 10(1/.25)  = 10/.25 = 40mg

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/