I've read the projections are that world population will peak in 2050 at about 10-11 billion people.

Also the maximum growth rate of the world's population occurred in 1965, amazingly. The rate of exponential growth has been slowing ever since. We're probably on an S curve that will flatten out toward the end of our lives, and we'll see a relatively stable world population for the first time in world history potentially. That will cause huge changes in world culture.