  A complete set of exact analytic solutions to the mode equation is found in
the region exterior to the acoustic horizon for a class of 1D Bose-Einstein
condensate (BEC) acoustic black holes. From these, analytic expressions for the
scattering coefficients and gray-body factor are obtained. The results are used
to verify previous predictions regarding the behaviors of the scattering
coefficients and gray-body factor in the low frequency limit.
