The planet Earth has problems that humans can solve, including a lot of environmental problems, energy problems, etc. On the other hand, an array of problems are beyond our ability to solve. One of them is to modify population growth trends. All the education programs, all the contraceptive programs, etc. cannot modify the attitude/habits that the human race has towards making babies.
Yes, population growth is exponential, the question is "what is the exponent". You can have negative exponential growth, as is the case in Europe. Clearly, in each country feel differently about their environment - which in turn reflects the number of children a woman will bear in her lifetime. The mindset of a men and a women with regard to children has so many variables, it is impossible to make accurate projections on a micro scale.
However, on a global basis, you don't need a mathematical statistics program to see that rate of growth (second derivative), has come to a halt. The world's population is continuing to grow. But it is rate of growth is slowing.
The interesting (and unknowable) question is "what happens when births = death?, or popultion growth = x^1. Scientists guess that the earth's population will = 10 billion. Nobody knows if the growth exponent will drop below 1, meaning the earth population will drop, or if the growth rate starts to increase again.
