SOLUTION: A particular drug can be administered via an IV to a patient so that the concentration
of the drug in the bloodstream jumps almost immediately to its highest level. The concentrat
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of the drug in the bloodstream jumps almost immediately to its highest level. The concentrat
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Question 930634: A particular drug can be administered via an IV to a patient so that the concentration
of the drug in the bloodstream jumps almost immediately to its highest level. The concentration
then decays exponentially. The half-life of this particular drug is 75 minutes and the effective range
of concentration for the drug in the bloodstream is from 1.5mg/ml to 3mg/ml. If an initial dose
of 100cc of solution containing the drug is given at 2pm, causing the concentration of the drug in
the bloodstream to spike to 3mg/ml. When should the next dose be given? Should the same dose be
given? If not, what percentage of the initial dose should be given? Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! We should give that patient the next dose when the level in his bloodstream is 1.5mg/mL.
The blood level will be be reduced to 1.5mg/mL = (1/2)(3mg/mL)
in 1 half-life = 75 minutes = 1 hour + 15 minutes, at 3:15PM.
At that point, we should give a dose large enough to raise his blood level back to 3mg/mL.
That requires a rise in blood concentration of 3mg/mL - 1.5mg/mL = 1.5mg/mL,
and we can assume that a blood level rise of 1.5mg/mL = (1/2)(3mg/mL) requires
1/2 of the original dose that caused a rise of 3mg/mL.
So the next dose will be 1/2 or 50% of the initial dose.
NOTE:
You may be thinking of formulas from the textbook.
They are not needed on this case, and memorizing them is not needed either. is intuitive and gets you to and to
