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.