We have studied effects of interspecies attraction in a Fermi-Bose mixture over a large regime of particle numbers in the 40K−87Rb system. We report on the observation of a mean-field driven collapse at critical particle numbers of 1.2×106 87Rb atoms in the condensate and 7.5×105 40K atoms consistent with mean-field theory for a scattering length of aFB=−284a0. For large overcritical particle numbers, we see evidence for revivals of the collapse. Part of our detailed study of the decay dynamics and mechanisms is a measurement of the (87Rb−87Rb−40K) three-body loss coefficient K3=(2.8±1.1)×10−28 cm6/s, which is an important parameter for dynamical studies of the system.