### 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 (109 Kg) is receiving an IV bolus administration of a drug. The plasma concentration was found to be 2.94 mg/L, when the blood was first collected. If the drug follows a first order elimination and the elimination rate constant (k) is 0.117 h-1, then how long will it take to reach the plasma concentration to 0.841 mg/L? Click on the button below to see the answer and explanations

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lb equals 10.7 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(2.94/0.841))/0.117
Or, t = 10.7
Thus, required time is 10.7 \quad h.(Ans).

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