Growth Model Help

["dale6998"]

1000 space aliens invaded a planet and started to multiply. Each one of
them wanders randomly, but whenever it bumps into another one they
instantly produce a baby alien who immediately grows up. So in a year
there were already 1500 aliens. Develop a model of the population
growth. Aliens promise to leave when their number reaches 3,000,000.
When will it happen?

Good Luck,

-D