I may have waited too long, since I did not give notice until after I had located a new place (always like to have a boat before I burn the bridge!) So it was probably a couple of weeks after they notified me of the rent increase before I sent my termination notice. So it sounds like my lack of direct response constitutes a tactit acceptance of the new lease terms, i.e. I have to pay the higher rent.
Now the office personnel are telling me that instead of prorating, they charge for a full month if my move date is after the 20th of the month (which it is). Cest la vie, right?

