The chemical evolution of the Milky Way is investigated using a dual-phase metal-enriched infall model in which primordial gas fuels the earliest epoch of star formation, followed by the ongoing formation of stars from newly accreted gas. The latest metallicity distribution of local K-dwarfs is reproduced by this model, which allows the Galactic thin disk to form from slightly metal-enriched gas with α-element enhancement. Our model predicts ages for the stellar halo and thin disk of 12.5 and 7.4Gyr respectively, in agreement with empirically determined values. The model presented in this paper is compared with a similar dual-phase infall model from Chiappini et al. (2001). We discuss a degeneracy that enables both models to recover the K-dwarf metallicity distribution while yielding different star formation histories. The metallicity distribution function (MDF) of K-dwarfs is proposed to be more directly comparable to chemical evolution model results than the G-dwarf distribution because lower mass K-dwarfs are less susceptible to stellar evolutionary effects. The K-dwarf MDF should consequently be a better probe of star formation history and provide a stronger constraint to chemical evolution models than the widely used G-dwarf MDF. The corrections that should be applied to a G-dwarf MDF are quantified for the case of the outer halo of NGC 5128.