@Aird12. This increase also allows for additional systematic uncertainties in our model, such as the possible contribution of unobscured sources. In Figure \[fig:xlf\_modA\] we compare the prediction assuming our model A for the specific accretion rate distribution (thick black line with the solid grey region indicating the uncertainty) with the observational constraints on the XLF (green hatched region). Our simple, observationally motivated model is able to successfully reproduce the faint-end of the XLF at all redshifts to $z\sim0.7$. The predominant evolution with redshift is accounted for by the strong evolution in the normalization of $p(\lambda {\;|\;}{\mathcal{M}_*},z)$, which produces a change in the normalization of our predicted XLF. However, we fail to reproduce the correct behavior at the bright end of the XLF ($L_\mathrm{X}\gtrsim10^{44.5}$ [$\mathrm{erg\;s^{-1}}$]{}). Our model predicts an exponential decline in the XLF at high luminosities, a consequence of the Schechter form of the galaxy SMF and the sharp cutoff we apply in the specific accretion rate distribution. We note that our model does not reproduce any of the (relatively minor) changes that may be observed in the evolution of the faint-end slope of the XLF with redshift nor any change in the break of the XLF. At $z\gtrsim0.7$ we 