  We explore the idea that the Type Ia supernovae (SNe Ia) rate consists of two
components: a prompt piece that is proportional to the star formation rate
(SFR) and an extended piece that is proportional to the total stellar mass. We
fit the parameters of this model to the local observations of Mannucci and
collaborators and then study its impact on three important problems. On cosmic
scales, the model reproduces the observed SNe Ia rate density below z=1, and
predicts that it will track the measured SFR density at higher redshift,
reaching a value of 1-3.5 X 10^-4 per yr per Mpc^3 at z=2. In galaxy clusters,
a large prompt contribution helps explain the iron content of the intracluster
medium. Within the Galaxy, the model reproduces the observed stellar [O/Fe]
abundance ratios if we allow a short (approximately 0.7 Gyr) delay in the
prompt component. Ongoing medium-redshift SN surveys will yield more accurate
parameters for our model
