Why do prairie grasses grow soon after a fire?

Grasses have growth points that are so close to the soil (hidden beneath leaf litter from other grasses) that a fire raging over the grassland doesn't reach this growth point; nor can it. Fire produces more carbon and organic matter, as well as minerals for the grass to grow from, hence the rapid growth after a fire. Also, a fire tends to eradicate all the old growth that the new grasses would have a harder time punching through, increasing the sunlight penetration to these new tillers, and consequently increasing forage growth.