### T08) Find t from Ct, C0 and half-life

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 (191 Kg) is receiving an IV bolus administration of a drug. The plasma concentration was found to be 2.56 mg/L, when the blood was first collected. If the drug follows a first order elimination and the elimination half life (t1/2) is 2.9 hr, then how long will it take to reach the plasma concentration to 1.513 mg/L?

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lb equals 2.2 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 ..... (1)
However, the question did not provide k, but we can derive it from:
k=0.693/t_{1/2}=0.693/2.9.
Plugging values in equation (1),
t =(ln(2.56/1.513))/(0.693/2.9)
Or, t = 2.2
Thus, required time is 2.2 \quad h.(Ans).

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