Total activity increase as a function of time during radioactive decay

During radioactive decay of a collection of nuclides the possibility of the total activity increasing is implicit in the standard differential equations. Traditional treatments do not emphasize this possibility so leading to unease when such a rise is observed. Examples of increases in activity for materials following irradiation by neutrons are given, and the phenomenon is explored in a model system of three nuclides. Conditions on the decay constants and the initial number of atoms of the nuclides such that the total activity can increase with time are given.