One class of models of hair cell synaptic function that has been investigated in recent years consists of one or more reservoirs of synaptic material connected to other reservoirs and/or the synaptic cleft by means of diffusion paths. One such general model is considered here, comprising two reservoirs and a global source of synaptic material connected in series and releasing material into the synaptic cleft by a diffusion path characterized by an intensity-dependent permeability. The explicit form of the solution of the model for a sudden onset of stimulation is derived: The solution comprises two exponentially decaying terms plus a constant. This solution is shown to have a unique inverse. This allows the determination of the parameters of the model directly from experimental data from auditory-nerve fibers in the Mongolian gerbil. The behavior of the derived model parameters with variation of stimulus intensity is demonstrated, and implications for synaptic function are discussed.