Once the bacteria reach some limit of saturation, they can only multiply as fast as they can geographically spread to new area. If they have some maximum speed

Once the bacteria reach some limit of saturation, they can only multiply as fast as they can geographically spread to new area. If they have some maximum speed of physical spread, then that limits them to a maximum speed of n^2 in two dimensions, or n^3 in three dimensions. If you think they're going to keep up exponential growth long enough to make a difference, that implies that you think they'll spread faster and faster across the lab, like a bad movie.