  We analyze V, I and H band HST images and two seasons of R-band monitoring
data for the gravitationally lensed quasar SDSS0924+0219. We clearly see that
image D is a point-source image of the quasar at the center of its host galaxy.
We can easily track the host galaxy of the quasar close to image D because
microlensing has provided a natural coronograph that suppresses the flux of the
quasar image by roughly an order of magnitude. We observe low amplitude,
uncorrelated variability between the four quasar images due to microlensing,
but no correlated variations that could be used to measure a time delay. Monte
Carlo models of the microlensing variability provide estimates of the mean
stellar mass in the lens galaxy (0.02 Msun < M < 1.0 Msun), the accretion disk
size (the disk temperature is 5 x 10^4 K at 3.0 x 10^14 cm < rs < 1.4 x 10^15
cm), and the black hole mass (2.0 x 10^7 Msun < MBH \eta_{0.1}^{-1/2}
(L/LE)^{1/2} < 3.3 x 10^8 Msun), all at 68% confidence. The black hole mass
estimate based on microlensing is consistent with an estimate of MBH = 7.3 +-
2.4 x 10^7 Msun from the MgII emission line width. If we extrapolate the
best-fitting light curve models into the future, we expect the the flux of
images A and B to remain relatively stable and images C and D to brighten. In
particular, we estimate that image D has a roughly 12% probability of
brightening by a factor of two during the next year and a 45% probability of
brightening by an order of magnitude over the next decade.
