The solution of the differential equations for the time rate of change of the activity induced in a foil detector by a neutron flux is revised. Generalized expressions of activity and number of disintegrations are reported for the case in which the neutron flux is intermittent in a non-periodic fashion, not constant during the pulse and multiple decays occur in the foil. Cases of practical application to fission reactors, to pulsed fusion machines, including hybrid reactors, and to cyclic activation are pointed out and briefly discussed.