The neutron generation time tgen in a reactor is the average time needed for a fast neutron emitted in one fission event to be slowed to thermal energies by the moderator and then initiate another fission event. Suppose the power output of a reactor at time t = 0 is P0. Show that the power output a time t later is P(t), where P(t) = P0kt/tgen and k is the multiplication factor. For constant power output, k = 1.