  We use semi-analytic techniques to evaluate the burst sensitivity of designs
for the EXIST hard X-ray survey mission. Applying these techniques to the
mission design proposed for the Beyond Einstein program, we find that with its
very large field-of-view and faint gamma-ray burst detection threshold, EXIST
will detect and localize approximately two bursts per day, a large fraction of
which may be at high redshift. We estimate that EXIST's maximum sensitivity
will be ~4 times greater than that of Swift's Burst Alert Telescope. Bursts
will be localized to better than 40 arcsec at threshold, with a burst position
as good as a few arcsec for strong bursts. EXIST's combination of three
different detector systems will provide spectra from 3 keV to more than 10 MeV.
Thus, EXIST will enable a major leap in the understanding of bursts, their
evolution, environment, and utility as cosmological probes.
