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We present 24 micron photometry of the intermediate-age open clusterPraesepe. We assemble a catalog of 193 probable cluster members that aredetected in optical databases, the Two Micron All Sky Survey (2MASS), and at 24micron, within an area of ~ 2.47 square degrees. Mid-IR excesses indicatingdebris disks are found for one early-type and for three solar-type stars.Corrections for sampling statistics yield a 24 micron excess fraction (debrisdisk fraction) of 6.5 +- 4.1% for luminous and 1.9 +- 1.2% for solar-typestars. The incidence of excesses is in agreement with the decay trend of debrisdisks as a function of age observed for other cluster and field stars. Thevalues also agree with those for older stars, indicating that debris generationin the zones that emit at 24 micron falls to the older 1-10 Gyr field starsample value by roughly 750 Myr.  We discuss our results in the context of previous observations of excessfractions for early- and solar-type stars. We show that solar-type stars losetheir debris disk 24 micron excesses on a shorter timescale than early-typestars. Simplistic Monte Carlo models suggest that, during the first Gyr oftheir evolution, up to 15-30% of solar-type stars might undergo an orbitalrealignment of giant planets such as the one thought to have led to the LateHeavy Bombardment, if the length of the bombardment episode is similar to theone thought to have happened in our Solar System.  In the Appendix, we determine the cluster's parameters via boostrap MonteCarlo isochrone fitting, yielding an age of 757 Myr (+- 36 Myr at 1 sigmaconfidence) and a distance of 179 pc (+- 2 pc at 1 sigma confidence), notallowing for systematic errors.

The low level of debris disk activity at the time of the Late Heavy Bombardment: a Spitzer study of Praesepe