Based on the recently developed numerical approach to understand the formation and the chemical evolution of the milky-way galaxy in the solar neighborhood we study the influence of the supernova type SN Ia rates on the galactic chemical evolution. Supernova SN Ia plays an important role in producing the iron inventory of the galaxy. We also study the dependence of the chemical evolution on the star formation rate prevailing during the initial one billion years of the evolution of the galaxy. This era marks the formation of the galactic halo and the thick disk. A comparison of the elemental abundance distributions of the dwarf stars in the solar neighborhood is made among the various models simulated in the present work. In order to explain the majority of the observed elemental evolutionary trends, specifically those related with the galactic evolution of iron and oxygen, it would be essential to incorporate a major component of prompt SN Ia to the galactic evolution. The prompt SN Ia would produce significant fraction of SN Ia within the initial ~100 million years from the time of star formation. The essential requirement of prompt SN Ia would result in a significant enhancement of SN Ia rates during the earliest epoch of the galaxy. The elemental evolutionary trends also favor an enhancement in the star formation rate during the initial one billion years of the galaxy at least by a factor of three compared to the trend prevailing during the latter evolutionary time of the galaxy.