Bees in a Certain Region Are Born at a Rate

Short Answer

Bees in a certain region are born at a rate that is proportional to their current population. Without any outside factors the population doubles in 3 weeks' time. It was observed that each day 12 bees joined the population, 10 were caught by men, and 5 died of natural causes.
Determine whether the population will survive if initially it counted 100 bees. If not, when will it die out?