A population of insects is allowed to grow in a experimental environment. The rate of increase of the population is proportional to the number, n, of insects, at any time t days after the start of the experiment. Regarding n and t as continuous variables, form a differential equation relating n and t, and solve it to show that n=Ae^kt, where A and K are constants. The net increases during the fourth and fifth days are 350 and 500 insects respectively. Determine the population at the beginning of the fourth say. Hence, or otherwise, determine the population at the beginning of the first day