What might the ideal population graph for humans look like over the next 200 years?

It took from the beginning of time until 1850 for the world's population to reach 1 billion. By 1900, it had doubled, by 1930, it had reached 3 billion, sometime in the 1960's, 4 billion, 1980's, 5 billion, and today we're over 6 billion.  Curiously, the Industrial Revolution was in full swing in Europe and North America in 1850; the rising standard of living initally increased population. However, as industrialization in a particular country continued, births declined, due to the shift from an agrarian to industrial economy; manpower began to be replaced by machinery.  Right now, the two most populous countries on Earth, China and India, together have over half the population of the world.  Both these giants are finally beginning to industrialize; as they do so, their population will eventually decrease.  Within 200 years, we should be at a sustainable level, which may be around 2 to 3 billion. So the population graph, which loped along until 1850, has spiked from then until now, will most likely continue to spike for a time (50 years?) then should slide down and level out over the next 150.