Final answer:
Bacteria with the trp operon will grow in tryptophan-rich agar, but will not synthesize tryptophan due to the repressible nature of the operon that turns off expression when tryptophan is abundant.
Step-by-step explanation:
When bacteria with a tryptophan (trp) operon are grown in an agar enriched with tryptophan, the bacteria will grow but will not synthesize tryptophan. This is because the trp operon is a repressible operon that is turned off when environmental tryptophan is abundant.
The presence of tryptophan activates a repressor protein which binds to the operator sequence, blocking RNA polymerase from transcribing the genes necessary for tryptophan synthesis. Therefore, gene expression related to the trp operon is halted, conserving the bacteria's resources.