According to a logistic model based on the assumption that the earth can support no more than 40 billion people, the world’s population (in billions) t years after 1960 is given by a function of the form

where C and k are positive constants. Find the function of this form that is consistent with the fact that the world’s population was approximately 3 billion in 1960 and 4 billion in 1975. What does your model predict for the population in the year 2010? Check the accuracy of the model by consulting the Internet.

P(t) = 40 1 + Cekt