There's a nicely illustrative video by Hans Rosling here: https://www.youtube.com/watch?v=fTznEIZRkLg on the population growth.
There are a lot of unproven assumptions there, such as that the education is a decreasing factor of population growth. That is only a correlation. I don't claim to know exactly how things are revolving in this matter, but as an educated guess I can say that, outside the necessary physical conditions (like enough nourishment and such), the culture of family is the most influential here. The education and the opportuni…
You can look at the the other videos of Hans Rosling which might answer that. Whether it's a correlation and not a cause might still be up for debate, but the observation of that effect have been observed in virtually all places around the world.