We present chemical abundance measurements of two metal-poor red giant stars in the ultra-faint dwarf galaxy Bootes I, based on Magellan/MIKE high-resolution spectra. For Boo I-980, with [Fe/H]=-3.1, we present the first elemental abundance measurements while Boo I-127, with [Fe/H]=-2.0, shows abundances in good agreement with previous measurements. Light and iron-peak element abundance ratios in the two Bootes I stars, as well as those of most other Boootes I members, collected from the literature, closely resemble those of regular metal-poor halo stars. Neutron-capture element abundances Sr and Ba are systematically lower than the main halo trend, and also show a significant abundance spread. Overall, this is similar to what has been found for other ultra-faint dwarf galaxies. We apply corrections to the carbon abundances (commensurate with stellar evolutionary status) of the entire sample and find 21% of stars to be carbon-enhanced metal-poor (CEMP) stars, compared to 13% without using the carbon correction. We reassess the metallicity distribution functions (MDF) for the CEMP stars and non-CEMP stars, and confirm earlier claims that CEMP stars might belong to a different, earlier population. Applying a set of abundance criteria to test to what extent Bootes I could be a surviving first galaxy suggests that it is one of the earliest assembled systems that perhaps received gas from accretion from other clouds in the system, or from swallowing a first galaxy or building block type object. This resulted in the two stellar populations observable today.
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