Why can't exponential growth not be sustained for long in any population?

An exponential growth curve is an S-curve. It shows a
rapid increase and then eventually, it begins to remain stable. If any population
continued to grow exponentially, the resources it needed would be unable to sustain a
population that huge. There wouldn't be enough habitat, food and other resources to
maintain the population. Eventually, competition would increase and individuals would
die off or the population may even become extinct. The Kaibab deer of Arizona is an
example of exponential growth due to the fact that their predators, the wolves, coyotes
and bobcats were killed to protect the deer. Because their enemies in the habitat were
gone, their population exploded and eventually, competition for scarce food led to their
numbers decreasing dramatically.