1. A population of insects in a region will grow at a rate that is proportional to their current population. In the absence of any outside factors the population will increase by 10% every year. On any given year there is a net migration into the area of 300 insects and 100 are eaten by the local bird population and 100 die of natural causes. If there are initially 1000 insects in the area, after how many years will the population reach 3000? To receive full credit, clearly define your variables, develop the differential equation model, solve it and answer the asked question. Leave the final answer in exact form - no calculator