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Based on numerical simulations of gas-rich galaxy mergers, we discuss a model in which quasar activity is tied to the self-regulated growth of supermassive black holes in galaxies. Nuclear inflow of gas attending a galaxy collision triggers a starburst and feeds black hole growth, but for most of the duration of the starburst, the black hole is heavily obscured by surrounding gas and dust which limits the visibility of the quasar, especially at optical and UV wavelengths. Eventually, feedback energy from accretion heats the gas and expels it in a powerful wind, leaving a 'dead quasar'. Between buried and dead phases there is a window during which the galaxy would be seen as a luminous quasar. Because the black hole mass, radiative output, and distribution of obscuring gas and dust all evolve strongly with time, the duration of this phase of observable quasar activity depends on both the waveband and imposed luminosity threshold. We determine the observed and intrinsic lifetimes as a function of luminosity and frequency, and calculate observable lifetimes ~10 Myr for bright quasars in the optical B-band, in good agreement with empirical estimates and much smaller than the black hole growth timescales ~100 Myr, naturally producing a substantial population of 'buried' quasars. However, observed and intrinsic energy outputs converge in the IR and hard X-ray bands as attenuation becomes weaker and chances of observation greatly increase. We obtain the distribution of column densities along sightlines in which the quasar is seen above a given luminosity, and find that our result agrees remarkably well with observed estimates of the column density distribution from the SDSS for appropriate luminosity thresholds. (Abridged)