  We use the observed distribution of Eddington ratios as a function of
supermassive black hole (BH) mass to constrain models of AGN lifetimes and
lightcurves. Given the observed AGN luminosity function, a model for AGN
lifetimes (time above a given luminosity) translates directly to a predicted
Eddington ratio distribution. Models for self-regulated BH growth, in which
feedback produces a 'blowout' decay phase after some peak luminosity (shutting
down accretion) make specific predictions for the lifetimes distinct from those
expected if AGN are simply gas starved (without feedback) and very different
from simple phenomenological 'light bulb' models. Present observations of the
Eddington ratio distribution, spanning 5 decades in Eddington ratio, 3 in BH
mass, and redshifts z=0-1, agree with the predictions of self-regulated models,
and rule out 'light-bulb', pure exponential, and gas starvation models at high
significance. We compare the Eddington ratio distributions at fixed BH mass and
fixed luminosity (both are consistent, but the latter are much less
constraining). We present empirical fits to the lifetime distribution and show
how the Eddington ratio distributions place tight limits on AGN lifetimes at
various luminosities. We use this to constrain the shape of the typical AGN
lightcurve, and provide simple analytic fits. Given independent constraints on
episodic lifetimes, most local BHs must have gained their mass in no more than
a couple of bright episodes, in agreement with merger-driven fueling models.
