One of the ways of evolution is an adaptation to the environment. Bacteria as faster replicate, it can get really fast mutations, and when some bacteria are able to survive the medication, due to the small dose, they can develop resistance to it. It is enhanced by the overuse of antibiotics, even when there is not an infection that requires treatment.
So, even when the administration of low doses would act as a vaccine in a certain way, it is mostly due to their ability to mutate and to pass those genes to the offspring, and even to other bacteria that they develop the ability to survive to the antibiotics.
in this case, the answer would be C