Final answer:
In the presence of radioactive thymine, both daughter cells would end up having radioactive DNA after one replication cycle, indicating the semiconservative nature of DNA replication.
Step-by-step explanation:
If you are provided with an actively dividing culture of E. coli bacteria to which radioactive thymine has been added, and a cell replicates once in the presence of this radioactive base, DNA in both daughter cells would be radioactive. This scenario is similar to the classic experiments conducted by Meselson and Stahl, who used isotopes to study DNA replication. The radioactive thymine would be incorporated into the newly synthesized DNA strands during replication, leading to both daughter cells containing this marker, confirming the semiconservative nature of DNA replication.