Final answer:
A mutation inactivating the regulatory gene of a repressible operon like the trp operon in E. coli results in continuous transcription of the genes controlled by that regulator because the repressor protein cannot inhibit transcription.
Step-by-step explanation:
A mutation that inactivates the regulatory gene of a repressible operon, like the trp operon in an E. coli cell, would lead to the continuous transcription of the gene(s) controlled by that regulator. This happens because the repressor protein that is normally produced by the regulatory gene is inactive, thus cannot bind to the operator to inhibit transcription. As a result, RNA polymerase can continuously bind to the promoter and initiate transcription, leading to uninterrupted production of mRNA and subsequent protein synthesis.