School of Mathematics and Statistics The University of Sydney PHAR1812 Calculus Tutorial 2 1. A certain drug is diluted by the human body in such a way that the concentration level falls at a rate proportional to the existing level. It is found that 50% of the original drug content of a particular organ is gone after 10 hours. How much longer will it take before 90% of the original content has been eliminated? 2. One gram of procainimide hydrochloride is injected intravenously into a patient, This drug has an elimination half-life of 2.7 hours. How much drug is still in the body 12 hours after the injection? 3. For practical purposes, drugs are often regarded as having been completely eliminated from the body after 5 elimination half-lives. What percentage of the initial dose of a drug in fact remains in the body after 5 half-lives? 4. The formula y = Ae-kt describes exponential decay. Derive the following relationship between the half-life t 1 / 2 and the decay rate constant k : t 1 / 2
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