A population of fish in the lake grows at the rate proportional to its population. There are originally 600 fish in the lake and in the absence of any outside factors, the population will double in 4 months time (assume 4 weeks/month). Each week there is a net migration of 30 fish into the lake and predators eat 47 fish. Two months after this situation, something causes the population of the predators to increase and they will now eat 70 fish a week. The migration of fish into the lake does not change. Does the fish population survive this? If not when do they die out?