There are initially 500 insects in a certain area. The population increases at a rate proportional to the current population, and in the absence of other factors, the population increases to 1000 in 4 week(s). Each day 10 migrate into the area, 8 die from disease and predators eat 19. (a) Determine the population of insects in the area at any time t in weeks. P(t) = X (b) Determine if the insects die out. If they die out enter the time (in weeks) in which they die out below to at least 4 decimal places. If the insects do not die out then enter DNE for the answer.

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