  We present 24 micron photometry of the intermediate-age open cluster
Praesepe. We assemble a catalog of 193 probable cluster members that are
detected in optical databases, the Two Micron All Sky Survey (2MASS), and at 24
micron, within an area of ~ 2.47 square degrees. Mid-IR excesses indicating
debris disks are found for one early-type and for three solar-type stars.
Corrections for sampling statistics yield a 24 micron excess fraction (debris
disk fraction) of 6.5 +- 4.1% for luminous and 1.9 +- 1.2% for solar-type
stars. The incidence of excesses is in agreement with the decay trend of debris
disks as a function of age observed for other cluster and field stars. The
values also agree with those for older stars, indicating that debris generation
in the zones that emit at 24 micron falls to the older 1-10 Gyr field star
sample value by roughly 750 Myr.
  We discuss our results in the context of previous observations of excess
fractions for early- and solar-type stars. We show that solar-type stars lose
their debris disk 24 micron excesses on a shorter timescale than early-type
stars. Simplistic Monte Carlo models suggest that, during the first Gyr of
their evolution, up to 15-30% of solar-type stars might undergo an orbital
realignment of giant planets such as the one thought to have led to the Late
Heavy Bombardment, if the length of the bombardment episode is similar to the
one thought to have happened in our Solar System.
  In the Appendix, we determine the cluster's parameters via boostrap Monte
Carlo isochrone fitting, yielding an age of 757 Myr (+- 36 Myr at 1 sigma
confidence) and a distance of 179 pc (+- 2 pc at 1 sigma confidence), not
allowing for systematic errors.
