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Bees in a Certain Region Are Born at a Rate

Question 58

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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?

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