Population-growth dynamics are important in a variety of planning studies for areas such as transportation and water resource engineering. One of the simplest models of such growth incorporates the assumption that the rate of change of the population p is proportional to the existing population at any time t:

dp/dt = Gp

where G = a growth rate (per year). This model makes intuitive sense because the greater the population, the greater the number of potential parents. At time t = 0, an island has a population of 6000 people. If G = 0.075 per year, employ Heun’s method (with out iteration) to predict the population at t = 20 years, using a step size of 0.5 year. Plot p versus t on standard and semilog graph paper. Determine the slope of the line on the semilog plot. Discuss your results.