Which equation correctly describes the IV bolus concentration-time profile for a one-compartment model?

• A. C(t) = (Dose / Vd) × e^(−k t)
• B. C(t) = (Dose / Vd) × (1 − e^(−k t))
• C. C(t) = Dose × e^(−k t)
• D. C(t) = (Dose × Vd) × e^(−k t)

Answer: (A)

In an IV bolus given to a single-compartment body, distribution is instantaneous into the apparent volume of distribution and elimination follows first-order kinetics. This means the starting concentration is simply the dose divided by the volume of distribution, and it then decays exponentially with the elimination rate constant k. The correct expression is C(t) = (Dose / Vd) × e^(−k t). At t = 0, the concentration is Dose/Vd, and as time progresses the exponential term reduces the concentration according to k, with the half-life t1/2 = ln(2)/k. The rate constant k is linked to clearance by k = Cl / Vd, tying how quickly the drug is eliminated to how it’s distributed in the body.

Why the other forms don’t fit this scenario: removing the Vd division would yield a concentration that doesn’t have the correct units or initial scaling, since you’d be treatingDose as if it were already a concentration. A form with (1 − e^(−k t)) represents accumulation or infusion over time, not a single instantaneous bolus. Including a factor like Dose × Vd would mix units inappropriately (giving something with inconsistent dimensions for concentration).