One-compartment open model for intravenous administration

After a sufficiently long time, most or all of the dose D will have been excreted. The linear model for this system is described by the mass balance equation  

The differential equation can be solved straightforwardly, yielding an exponential function with respect to time  

Note that the solution is in terms of amounts Xp rather than observed plasma concentrations Cp. The conversion from amounts to concentrations is defined by means of  

The half-life time t of a drug is an important pharmacokinetic parameter. In this simple model it can be obtained immediately from the solution in eq. (39.6)  

The concentration-time curve can be integrated numerically and yields the so-called area under the curve (AUC)  

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