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where M_t is the constituent mass at the end of time step t, V_t is the storage volume at the end of time step t, and is the time step size. Equation 7 assumes that flux rates are constant during a time step and that the storage volume at the end of the time step is representative of the volume during the time step. It is more convenient to express the change in constituent mass with respect to the half-life h. An expression for the half-life can be derived for Equation 7 as:

Using the above expression, we can then express Equation 7 in terms of the half-life rather than the decay constant:

Equation 9 forms the basis of the Exponential Decay model in Source. The solution becomes less accurate as the half-life becomes smaller (particularly if the half-life is smaller than the time step) and as the flushing rate (Q_out /V_t+1) becomes larger. It also follows from Equation 9 that if V_t+1 = 0 then M_t+1 = 0.

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