SOLUTION: What is the maximum and minimum amount of a drug remaining in a patient
in the limit (that is, as time tends to infinity) given that the patient takes an 80 milligram dose once a
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-> SOLUTION: What is the maximum and minimum amount of a drug remaining in a patient
in the limit (that is, as time tends to infinity) given that the patient takes an 80 milligram dose once a
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Question 1173191: What is the maximum and minimum amount of a drug remaining in a patient
in the limit (that is, as time tends to infinity) given that the patient takes an 80 milligram dose once a day at the same time each day and the drug has a half life of 22 hours? Found 2 solutions by ikleyn, ewatrrr:Answer by ikleyn(52788) (Show Source):
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.
Hi
Using Half life Formula:
.5 = 80e^(-(22/24)k)
ln(.5)/(-22/24) = k
k = -.7562
Q(t) = 80e^(-.7562)t (t in days)
Takes basically 2 weeks for a daily dose taken previously to leave the body
Q(14days) = .002mg for example
total on board on the 14 day of dosing is 150.7844mg
Maximum: 150.8mg (desired maintenance level) same as previously determined
As to minimum, once one began with a single dose: Appears prior to 2nd dosage = 42.4mg
Found Interesting - already at 150.4mg on the 7th day of dosing...
Once 7th dosage has been taken:
80 7th dosage
37.5558 6th remaining
17.6304 5th remaining
8.2766 4th remaining
3.8854 3rd remaining
1.824 2nd remaining
.402 1st remaining
0.8563
150.4mg
Responded as was interested in mathematically watching it reach the maintenance level,
as am on a maintenance prescription for A Fib.
