Direct Action: the Integral
in the limit of DD and DN small, dN = -kNdD, where k is the ìinactivation constantî.
This gives us the usual differential equationdN/N = -kdD, which integrates tolnN = -kD + C, or N = e-kD * eC = N0e-kDwhere N0 = eC has the physical meaning of the number of molecules in the system (number undamaged before the damage began)
The inactivation constant has units of Gy-1 and is the reciprocal of the dose required to reduce the number of undamaged molecules by 1/e.