Final answer:
Bacteria with a plasmid containing an integrated eukaryotic gene would grow on a medium with ampicillin, as the plasmid confers resistance to this antibiotic. These cells can be distinguished by their lack of color change on media containing X-gal due to the disruption of the lacZ gene.
Step-by-step explanation:
Bacteria containing a plasmid into which the eukaryotic gene has integrated would grow on media that contains the antibiotic ampicillin. The plasmid carries a gene for resistance to this antibiotic. During the process of transformation, some bacterial cells do not take up plasmids at all; others take up nonrecombinant plasmids that do not have the foreign DNA. However, the key cells of interest are the few that take up recombinant plasmids containing both the eukaryotic gene and the ampicillin resistance gene.
Since the recombinant plasmid also disrupts the lacZ gene, which would normally produce an enzyme that metabolizes X-gal, a substrate that changes color in the presence of this enzyme, scientist can easily identify such bacteria. Bacteria with the recombinant plasmid show up as white colonies on a medium with ampicillin and X-gal, in contrast to blue colonies from bacteria with nonrecombinant plasmids. This selective process is crucial because it allows only the bacteria containing the recombinant plasmids to grow, which can then be harvested and cultured further for gene expression studies or other purposes.