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 176 Kg patient was intravenously administered a drug. The plasma concentration was found to be 0.66 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 `3.01 \quad h`, then determine the plasma concentration after 3.8 hours.


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lb equals 0.275 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/(3.01 h)=0.23 h^{-1}`.
    Plugging the values in this equation, we get:
    `C_{t}=0.66 × e^(- 0.23 × 3.8)`
    `∴ C_{t}=0.275`
    Thus, the later concentration is: 0.275 mg/L. (Ans).