When a population of organisms has the conditions to increase, mainly lack of predators and surplus food resources, it increases exponentially. That rapid increase in the population doesn't lats for very long though. The reason why it can continue to grow as much as that the food resources are limited, so when the optimal number of organisms is on the scene in accordance to the available food sources, any further increase results in inner species competition for food. That will cause a significant decrease in the increase of the population, or even totally stop. The appearance of predators is also a factor, as the predators will increase in numbers in accordance to the amount of prey animals, so once they reach their optimal numbers then they will be able to control the population and its increase or decrease.
