### T06) Find half life from C0, Ct 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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For an intravenously administered drug, if the concentration at 2 hr is 4.3 mg/mL, and concentration at 4.9 hr is 2.649 mg/mL, then determine the elimination half life of the drug. Assume that the drug follows a first order kinetics. Click on the button below to see the answer and explanations

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lb equals 4.15 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
∴ k = ln(C_{0}/C_{t})/t
Difference between two time points (4.9 hr and 2 hr) is 2.9 hr.
\implies k =(ln(4.3/2.649))/2.9
Or, k = 0.167
Thus, the rate constant is 0.167 \quad h^{-1}.
Now, to calculate the half life from rate constant: t_{1/2}=0.693/k=0.693/(0.167 \quad h^(-1))=4.15 \quad h (Ans).

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