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 million 87Rb atoms in the condensate and 750,000 40K atoms consistent with mean field theory for an interspecies scattering length of -281(15) Bohr radii [S. Inouye et al., Phys. Rev. Lett. 93, 183201 (2004)]. For overcritical particle numbers, we see evidence for revivals of the collapse. Before and after the collapse, the axial expansion profileof the 40K cloud is strongly modified and reflects the in-trap density profile distorted by the mean field interspecies attraction. 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 cm^6/s, which is an important input parameter for dynamical studies of the system.