Population Growth When predicting population growth, demographers must consider birth and death rates as well as the net change caused by the difference between the rates of immigration and emigration. Let P be the population at time t and let N be the net increase per unit time resulting from the difference between immigration and emigration. So, the rate of growth of the population is given by
where N is constant. Solve this differential equation to find P as a function of time, when at time t = 0 the size of the population is P0.
(b) Use the logistic model to estimate the world population in the year 2000. Compare with the actual population of 6.1 billion. (Round the answer to two decimal places.) P =
(c) Use the logistic model to predict the world population in the years 2100 and 2500. (Round your answer to two decimal places.)
(d) What are your predictions if the carrying capacity is 60 billion? (Round your answers to two decimal places.)
