### T02) Find Ct from C0, t-half and t

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 198 Kg patient was intravenously administered a drug. The plasma concentration was found to be 2.47 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 7.62 \quad h, then determine the plasma concentration after 2.9 hours.

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lb equals 1.897 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/(7.62 h)=0.091 h^{-1}.
Plugging the values in this equation, we get:
C_{t}=2.47 × e^(- 0.091 × 2.9)
∴ C_{t}=1.897
Thus, the later concentration is: 1.897 mg/L. (Ans).