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
Total tried: Correct: Wrong:
A patient (158 Kg) is receiving an IV bolus administration of a drug. The plasma concentration was found to be 4.57 mg/L, when the blood was first collected. If the drug follows a first order elimination and the elimination half life (t1/2) is 5.1 hr, then how long will it take to reach the plasma concentration to 3.829 mg/L?
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lb equals 1.3 h kg
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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}=0.693/5.1`.
Plugging values in equation (1),
`t =(ln(4.57/3.829))/(0.693/5.1)`
Or, `t = 1.3`
Thus, required time is `1.3 \quad h`.(Ans).