We report the effect of nonmagnetic Ti4+ impurities on the electronic and magnetic properties of Sr3Ru2O7. Small amounts of Ti suppress the characteristic peak in magnetic susceptibility near 16 K and result in a sharp upturn in specific heat. The metamagnetic quantum phase transition and related anomalous features are quickly smeared out by small amounts of Ti. These results provide strong evidence for the existence of competing magnetic fluctuations in the ground state of Sr3Ru2O7. Ti doping suppresses the low-temperature antiferromagnetic interactions that arise from Fermi surface nesting, leaving the system in a state dominated by ferromagnetic fluctuations.