We analyze the nonlinear, non-stationary radiation trapping process in a cell filled with a noble gas and an alkali vapor excited by a short intense laser pulse. We derive analytical approximations for the total density of the excited atoms, and for the radiation emerging from the cell. The considered lineshapes are pure Doppler, Voigt, and pure Lorentzian profiles. We confirm that the emergent radiation can decay faster than with the natural lifetime of the atomic transition. We also show that as we increase the noble gas pressure, the decay of the emergent radiation becomes slower at early times and faster at late times.