Was the bottle half full at 11:30?

That would be the correct answer... if the bottle filled the same amount every minute. For instance, if we were filling it from a dripping water faucet, the bottle would be 1/4 full after 1/4 of the time, half full after half the time, and completely full after all the time had passed.

But that's not what's going on here, because the bacteria double their numbers every minute.