### T03) Find C0 from Ct, k 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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A 114 -kg patient has received an IV bolus injection of a drug. A sample of blood was collected 8 hours after the first collection. The drug follows a first order elimination process, and its elimination rate constant is 0.13 \quad h^{-1}. If the plasma concentration was 0.65 mg/L in the second sample, then what was the concentration in the initial sample? Click on the button below to see the answer and explanations

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lb equals 1.84 mg/L kg

For a first order process,
C_{t}=C_{0}×e^(-kt)
It may be re-organized as:
C_{0}=C_{t}/(e^(-kt))
Or, C_{0}=C_{t}×e^(kt)
Plugging the values in above equation, we get:
C_{0}=0.65 × e^(0.13 × 8)
∴ C_{0}=1.84
Thus, the initial concentration was: 1.84 mg/L. (Ans).

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