Prof,
If the resistance to antibiotics was not already present the entire culture would die. By introducing antibiotics you are creating a catastrophic event. Even viruses such as HIV have had drug resistant strains before drug therapy even began. This is not to say that bacterial mutations cannot happen but they are usually a degenerative change as in the loss of a control gene that may cause resistance to penicillin by producing excessive amounts of penicillinase. Even beneficial plasmid transfer must be existent.
Anyway, this is not a selectively adapted response to man-made drugs and I hope this is not what youre implying
You start with one cell. That cell is not resistant. It divides. You have two cells. In all probability neither is resistant. Ditto four cells. As the population grows exponentially, the small probability of a favorable mutation is multiplied by the large number of cells (and perhaps increased by the presence of mutagens). Eventually, in a culture of a billion cells, a few have become resistant. Expose the culture to antibiotics, and the resistant cells survive, and eventually take over the culture.
The possibility of a mixed culture is eliminated by making sure the culture is monoclonal; i.e. - you start with a single bacterium. Any diversity after that has arisen by mutation.