The global population over the course of the past 50 years, as modeled above, regresses to closely match the graph of a logistic function. Growth has begun to consistently slow down, starting just before 2000, where the inflection point of the regression above is located. The upper bound on the graph above is just over 10.22 billion people, over two and a half billion more people than currently are alive. However, few estimates of the Earth's carrying capacity for human population are that high. Most estimates of carrying capacity, when taking into account capacity for food production and other crucial factors, estimate that the planet can sustain somewhere between 9 billion and 11 billion people. If one assumes the capacity to be approximately 10 billion, the population will reach that point in 2054 if it continues to follow the trend of the logistic function above, which it has done very closely for over 60 years. At that point, the population may continue to grow slowly, but at that point it will no longer be sustainable. A rise in mortality rates would likely accompany a rise in population at that point, and the population would gravitate back towards its final carrying capacity.
Information and data from:
worldometers.com
https://www.livescience.com/16493-people-planet-earth-support.html
http://www.bbc.com/earth/story/20160311-how-many-people-can-our-planet-really-support
worldometers.com
https://www.livescience.com/16493-people-planet-earth-support.html
http://www.bbc.com/earth/story/20160311-how-many-people-can-our-planet-really-support