Chapter D1, Problem 28RE

Logistic growth in India The population of India was 435 million in 1960 (t = 0) and 487 million in 1965 (t = 5). The projected population for 2050 is 1.57 billion.

a.    Assume that the population increased exponentially between 1960 and 1965, and use the populations in these years to determine the natural growth rate in a logistic model.

b.    Use the solution of the logistic equation and the 2050 projected population to determine the carrying capacity.

c.    Based on the values of r and K found in parts (a) and (b), write the logistic growth function for India’s population (measured in millions of people).

d.    In approximately what year does the population of India first exceed 2 billion people?

e.    Discuss some possible shortcomings of this model. Why might the carrying capacity be either greater than or less than the value predicted by the model?