Acotton farmer applies a new insecticide against the boll weevil to his crop for several years. at first, the treatment was successful, but then the insecticide became ineffective and the boll weevil rebounded. did evolution occur? explain.

Yes, it is possible that evolution occurs in this case.

At first, the new insecticide is effective against the boll weevil. Spraying the insecticide will kill the boll weevil in a way. The insecticide might attack boll weevil enzyme or any part of its organs.
But some of them might have a mutation that renders the insecticide ineffective. The mutation probably happens to DNA that code the enzyme or protein that targeted by the insecticide, makes the insecticide completely ineffective.
The next spray will kill all old organism, leaving the new resistant organism in less competition area. This will allow the resistant organism to grow fast and eventually replace all the old organism in the area.