Lesson A medication decay in a human's body

A medication decay in a human's body

Problem 1

Notice that the ratio of  16 mg/L  to  512 mg/L  is   =  = .


It means that after  5  (five)  half-life periods the original concentration 

of the drug in the plasma will decrease from the original  512 mg/L  to  16 mg/L.


So, the ANSWER to the problem's question is  5 times half-life periods, or 5 x 16 hours = 80 hours.

Problem 2

Notice that  6.25%  is  this ratio   =  = .


It means that after 4 (four) half-life periods the amount of the drug in the body will reach 6.25% of the original level.


So, the ANSWER to the problem's question is  4 times the half-life period, or 4 x 3 hours = 12 hours.

Problem 3

Notice that the ratio of  320 mg of caffeine  to  5 mg of caffeine  is   =  = .


It means that after 6 (six) half-life periods the original amount of the caffeine

of the bloodstream will decrease from the original  420 mg  to  5 mg/L.


So, the ANSWER to the problem's question is  6 times the half-life period, or 6 x 5 hours = 30 hours.

Problem 4

The original amount was 200mg, and the half-life period of elimination from the body is 4 hours.

It means that the number of milligrams of the drug remaining in the body after t hours  is  .    ANSWER

Problem 5

The maximum amount    is the sum of the infinite Geom. progression 

with the first term  "a" = 80 milligrams  and the common ratio  r = 0.5^(24/22) = 0.469465


      =  =  = 150.7913  milligrams.


The minimum amount    is 80 milligrams less than , i.e   = 70.7913  milligrams.


As the time becomes very large, the process (the plot of the function d(t)) is periodical with the period of time equal to 24 hours.