Pictured below is the inducible soap operon of the pseudomonas species growing in the oncology ward. imagine the operator has been damaged such that the active repressor no longer binds to it. how would this damage affect the growth of pseudomonas?

The growth on soap would not change that much, it will just change a little or just a bit of its part, but the damage would decrease the species growth elsewhere. Growth on soap will not change, but the damage had the chance to decrease the species growth elsewhere.