We analyze membrane inlet mass spectrometry (MIMS) employing a hollow fiber membrane which selectively passes a low molar mass analyte dissolved in solution to a mass spectrometer. Two approximate solutions are developed to Fick's second law for a step-change in upstream concentration. The first, found by a finite Fourier transform, gives an accurate description of the MIMS signal at relatively long times while the second, found via Laplace transform, gives an accurate description at short times. Together with the steady-state solution, the results allow straightforward determination from data of the analyte's diffusivity in the membrane as well as the analyte partition partition coefficient between the upstream solution and the membrane. Analysis of data for trace levels of toluene in aqueous solution passed through a poly(dimethyl siloxane) (PDMS) hollow-fiber yields the diffusion coefficient, partition coefficient, and their temperature dependences for the toluene/PDMS system.