The growth rate of yeast is a function of temperature, as someone
mentioned upthread.

Growth rates of Yeast/LB bacteria can be found here

http://aem.asm.org/cgi/content/full/64/7/2616/F1

But! Please keep in mind ;

Cultured yeast needs oxygen to reproduce, so once it has depleted the
oxygen in a starter/sponge/dough, it has pretty much reached the
population it's going to have. After this, it shifts its metabolism to
anaerobic. In short ; No oxygen, no baby yeast .-)

To make sure your starter is at it's optimum for rising, it should
probably be stired once in a while, just to make sure that the yeast
has multiplied to it's maximum potential. It's also usefull to know
that the LB organism both reproduce and metabolise carbohydrates
without oxygen.