This statement is true because this statement tells us a very rational point of view as well as a fact that the growth of population increases very quickly for a certain point then after that it growth drops to zero.
The reason for the drop in the growth to zero is due to the many factors which is explained by the term "Carrying Capacity of Environment".
Carrying Capacity of an environment is very crucial for the people living in that environment. It is basically measure of the ability of the ecosystem to sustain itself by providing basic needs to maximum number of the human beings. The basic needs include shelter, food, water etc.
When a carrying capacity is reached, then its means that the maximum people are getting basic needs from the ecosystem. Then further increase in population results in the deficiency of the resources for food, water, shelter etc so, as a result that result in the decrease of population due to competition of survival and other factors.
