Chapter 28, Problem 22P

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:

$\frac{dp}{dt}=Gp\left(\text{P28}\text{.22}\text{.1}\right)$

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 (without 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.