The present population of Latin America is around 300 million, and many of them are under-nourished. But if the population continued to increase at the present rate, it would take less than 500 years to reach the point where the people, packed in a standing position, formed a solid human carpet over the whole area of the continent. This is so, even if we assume them to be very skinny - a not unrealistic assumption. In 1,000 years from now they would be standing on each other's shoulders more than a million deep. By 2,000 years, the mountain of people, travelling outward at the speed of light, would have reached the edge of the known universe.
It will not have escaped you that this is a hypothetical calculation! It will not really happen like that for some very good practical reasons. The names of some of the reasons are famine, plague, and war; or, if we are lucky, birth control.