We have obtained optical spectra of 29 early-type (E/S0) galaxies that hosted type Ia supernovae (SNe Ia). We have measured absorption-line strengths and compared them to a grid of models to extract the relations between the supernova properties and the luminosity-weighted age/composition of the host galaxies. The same analysis was applied to a large number of early-type field galaxies selected from the SDSS spectroscopic survey. We find no difference in the age and abundance distributions between the field galaxies and the SN Ia host galaxies. We do find a strong correlation suggesting that SNe Ia in galaxies whose populations have a characteristic age greater than 5 Gyr are ~ 1 mag fainter at V(max) than those found in galaxies with younger populations. However, the data cannot discriminate between a smooth relation connecting age and supernova luminosity or two populations of SN Ia progenitors. We find that SN Ia distance residuals in the Hubble diagram are correlated with host-galaxy metal abundance, consistent with the predictions of Timmes, Brown & Truran (2003). The data show that high iron abundance galaxies host less-luminous supernovae. We thus conclude that the time since progenitor formation primarily determines the radioactive Ni production while progenitor metal abundance has a weaker influence on peak luminosity, but one not fully corrected by light-curve shape and color fitters. Assuming no selection effects in discovering SNe Ia in local early-type galaxies, we find a higher specific SN Ia rate in E/S0 galaxies with ages below 3 Gyr than in older hosts. The higher rate and brighter luminosities seen in the youngest E/S0 hosts may be a result of recent star formation and represents a tail of the prompt SN Ia progenitors.
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