The total world population according to the International Program Centre (IPC), U.S. Bureau of
Census, is given in the table below for the years 1950-2050.
(a) Use the data of 1950-2000 only to construct an appropriate continuous model. Start with a
relevant word equation, define all variables you introduce, and give clear written explanations
on how you obtain the differential equation from the word equation.
(b) Solve the resulting differential equation with an appropriate initial condition.
(c) Construct a table and a graph comparing the population predicted by your model in part (a)
and (b) with the data. Comment on the results.
(d) Use your model to project the world population for the year 2050.
How does your result
compare with the IPC’s projection of 9,383,147,855? Is your model adequate as a model for
future projection of the world population? How would you improve the model?
Sample Solution
