Why does lac operon shut down some time after addition of lactose in the medium In the medium where E coli was growing lactose was added which induced the lac operon?

The lac operon in E. coli is initially activated in the presence of lactose, which is converted to allolactose, acting as an inducer that binds to the repressor protein and allows transcription of the genes needed for lactose metabolism. However, once lactose is consumed and its levels decrease, the concentration of allolactose drops, leading to the re-binding of the repressor to the operator region of the operon, thus shutting down transcription. Additionally, if glucose is present, it can inhibit lac operon expression through catabolite repression, further contributing to the shutdown.