### 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 189 Kg patient was intravenously administered a drug. The plasma concentration was found to be 4.42 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 28.88 \quad h, then determine the plasma concentration after 0.5 hours.

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lb equals 4.367 mg/L kg

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/(28.88 h)=0.024 h^{-1}.
Plugging the values in this equation, we get:
C_{t}=4.42 × e^(- 0.024 × 0.5)
∴ C_{t}=4.367
Thus, the later concentration is: 4.367 mg/L. (Ans).

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