We determine the contribution of AGN to the mid-IR emission of luminous infrared galaxies (LIRGs) at z>0.6 by measuring the mid-IR dust continuum slope of 20,039 mid-IR sources. The 24 micron sources are selected from a Spitzer/MIPS survey of the NOAO Deep Wide-Field Survey Bootes field and have corresponding 8 micron data from the IRAC Shallow Survey. There is a clear bimodal distribution in the 24 micron to 8 micron flux ratio. The X-ray detected sources fall within the peak corresponding to a flat spectrum in nufnu, implying that it is populated by AGN-dominated LIRGs, whereas the peak corresponding to a higher 24 micron to 8 micron flux ratio is likely due to LIRGs whose infrared emission is powered by starbursts. The 24 micron emission is increasingly dominated by AGN at higher 24 micron flux densities (f_24): the AGN fraction of the z>0.6 sources increases from ~9% at f_24 ~ 0.35 mJy to 74+/-20% at f_24 ~ 3 mJy in good agreement with model predictions. Deep 24 micron, small area surveys, like GOODS, will be strongly dominated by starburst galaxies. AGN are responsible for ~ 3-7% of the total 24 micron background.
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