For most drugs given intravenously, a body metabolizes the drug at a rate propor

Question

For most drugs given intravenously, a body metabolizes the drug at a rate proportional to the amount of the drug present. Suppose that 30cc of a drug is given, and that 2 hours later, a blood test indicates that 25cc remains. What is the "half-life" of the drug? Suppose that the drug is effective as long as at least 6cc are present. When will this threshold be reached? Suppose further that serious side effects occur if more than 40cc of the drug are present. That is, the effective safe range of the drug is from 6cc to 40cc. Determine a dosage and time schedule that is reasonable for maintenance.

Explanation / Answer

1) Since 1st order kinetics is followed.Thus, the governing equation is :-

k*t = ln{[A0]/[A]}

or, k*2 = ln(30/25)

or, rate constant, k = 0.0912 hr-1

half life = ln2/k = 7.6 hours

2) k*t = ln{[A0]/[A]}

or, 0.0912*t = ln(30/6)

or, time ,t to reach the threshold = 26.3 hours

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