Final answer:
Initially, both the ampicillin and the non-ampicillin liquid cultures will contain a mix of ampicillin-resistant and non-resistant bacteria. With time, the culture containing ampicillin should select for resistant bacteria, increasing their ratio in comparison to the non-resistant ones. Cultures without ampicillin may also develop resistance over time, but at a significantly lower rate.
Step-by-step explanation:
When bacteria are transformed with a plasmid containing an ampicillin-resistance gene, we expect ampicillin-resistant bacteria to survive and grow in the presence of the antibiotic. However, non-resistant bacteria will not. In the initial assay of both liquid cultures (one with ampicillin and one without), the liquid culture without ampicillin will show growth of both resistant and non-resistant bacteria. Whereas the culture with ampicillin will primarily show the resistant ones, provided that the transformation was successful.
Over time, as the bacteria continue to grow in liquid culture, the culture without ampicillin should still contain a mixture of resistant and non-resistant bacteria. However, the ampicillin-containing culture should enrich for ampicillin-resistant bacteria. When plated on LB plates with ampicillin after an extended period, we would expect to see a higher ratio of ampicillin-resistant bacteria due to selective pressure from the antibiotic.
If there are any mutations or horizontal gene transfer that confer resistance, the culture without ampicillin might also show an increased number of resistant colonies over time, but this would typically be at a much lower frequency compared to the culture with ampicillin where the selective pressure is constant.