We use a rate equation model in order to reproduce the dynamics of two-dimensional excitons and free carriers in a time resolved photoluminescence experiment. We investigate the dynamics of the exciton formation from free electron-hole pairs, and the evolution of Is excitons within their band. The interaction of excitons and free carriers with optical and acoustic phonons is considered. The shape of the time resolved photoluminescence signal is considerably different in the case of acoustic or optical phonon assisted formation. An analysis of the photoluminescence rise as a function of the lattice temperature and carrier density is reported.