T03) Find C0 from Ct, k 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 125 -kg patient has received an IV bolus injection of a drug. A sample of blood was collected 11.5 hours after the first collection. The drug follows a first order elimination process, and its elimination rate constant is `0.081 \quad h^{-1}`. If the plasma concentration was 0.453 mg/L in the second sample, then what was the concentration in the initial sample?

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lb equals 1.15 mg/L kg

    For a first order process,
    It may be re-organized as:
    Or, `C_{0}=C_{t}×e^(kt)`
    Plugging the values in above equation, we get:
    `C_{0}=0.453 × e^(0.081 × 11.5)`
    `∴ C_{0}=1.15`
    Thus, the initial concentration was: 1.15 mg/L. (Ans).