T07) Find t from Ct, C0 and k

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 patient (89 Kg) is receiving an IV bolus administration of a drug. The plasma concentration was found to be 1.23 mg/L, when the blood was first collected. If the drug follows a first order elimination and the elimination rate constant (k) is 0.221 h-1, then how long will it take to reach the plasma concentration to 0.091 mg/L?


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lb equals 11.8 h kg

    For a first order process,
    `C_{t}=C_{0}×e^(-kt)`
    It may be re-organized as:
    `ln(C_{t})=ln(C_{0})-kt`
    `\implies t = ln(C_{0}/C_{t})/k`
    Plugging values in this equation,
    `t =(ln(1.23/0.091))/0.221`
    Or, `t = 11.8`
    Thus, required time is `11.8 \quad h`.(Ans).