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Charge transport in three-dimensional metal-halide perovskite semiconductors is due to a complex combination of ionic and electronic contributions, and its study is particularly relevant in light of their successful applications in photovoltaics as well as other opto- and microelectronic applications. Interestingly, the observation of field effect at room temperature in transistors based on solution-processed, polycrystalline, three-dimensional perovskite thin films has been elusive. In this work, we study the time-dependent electrical characteristics of field-effect transistors based on the model methylammonium lead iodide semiconductor and observe the drastic variations in output current, and therefore of apparent charge carrier mobility, as a function of the applied gate pulse duration. We infer this behavior to the accumulation of ions at the grain boundaries, which hamper the transport of carriers across the FET channel. This study reveals the dynamic nature of the field effect in solution-processed metal-halide perovskites and offers an investigation methodology useful to characterize charge carrier transport in such emerging semiconductors.