T01-10) Random from these types
50. Pharmacokinetics 50.2) Plasma concentrations over time 50.2.1) Plasma concentrations over time
T01: Later plasma concentration Normal 1
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A 72 Kg patient was intravenously administered a drug. The plasma concentration was found to be 3.69 mg/L, when the blood was first collected. If the drug follows a first order elimination and the plasma half-life of the drug is `9.12 \quad h`, then determine the plasma concentration after 7.6 hours.
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lb equals 2.071 mg/L kg
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For a first order process,
`C_{t}=C_{0}×e^(-kt)`
In the question, k is not provided, but we can derive it from the equation below:
`k=0.693/t_{½}=0.693/(9.12 h)=0.076 h^{-1}`.
Plugging the values in this equation, we get:
`C_{t}=3.69 × e^(- 0.076 × 7.6)`
`∴ C_{t}=2.071`
Thus, the later concentration is: 2.071 mg/L. (Ans).