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 Bo\"otes 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.Comment: 6 pages, accepted for publication in Ap