Why does the lac operon shut down some time after the addition of lactose in the medium where E.coli was growing ? Why low level expression of lac operon is always required ?

Explanation

Lac operon has polycistronic structural gene i.e., z, y, a adjacent to an operator, a promoter and a regulator.
`**" "`Lactose is the inducer that inactivates repressor, after addition of lactose, `beta-` galactosidese breaks lactose to galactose and glucose. Therefore, there is no more lactose to bind to the repressor protein and the lac operon shuts down.
`**" "`A very low level of expression of lac operon has to be present in the cell all the time, otherwise lactose cannot enter the cells.