A population of beetles in a region will grow at a rate that is proportional to their current population. On its own and without outside influence, the population will triple in two weeks time. On any given day there is a net migration into the area of 15 beetles, 16 are eaten by the local owl population, and 7 die of natural causes. If there are initially 100 beetles in the area will the population survive? If not, when do they die out? Make sure to completely describe the model you use to draw these conclusions.