  The Medusae Fossae Formation (MFF) is an enigmatic sedimentary unit near the
equator of Mars, with an uncertain formation process and absolute age. Due to
the heavily wind-eroded surface, it is difficult to determine the absolute
model age of the MFF using a one-parameter model based on the crater
size-frequency distribution function with existing crater count data. We create
a new two-parameter model that estimates both age and a constant erosion rate
($\beta$) by treating cratering as a random Poisson process. Our study uses new
crater count data collected from Context Camera imagery for both the MFF and
other young equatorial sedimentary rock. Based on our new model, the Central
MFF formed $>$1.5 Gyr ago and had low erosion rates ($<$650 nm yr$^{-1}$),
whereas the East MFF, Far East MFF, and Zephyria Planum most likely formed
$<$1.5 Gyr ago and had higher erosion rates ($>$740 nm $^{-1}$). The top of
Aeolis Mons (informally known as Mount Sharp) in Gale Crater and Eastern Candor
have relatively young ages and low erosion rates. Based on the estimated
erosion rates (since fast erosion permits metastable shallow ice), we also
identify several sites, including Zephyria Planum, as plausible locations for
shallow subsurface equatorial water ice that is detectable by gamma-ray
spectroscopy or neutron spectroscopy. In addition to confirming $<$1.5 Gyr
sedimentary rock formations on Mars, and distinguishing older and younger MFF
sites, we find that fast-eroding locations have younger ages and MFF locations
with slower erosion have older best-fit ages.
