Question

What are some factors that might stop a population's exponential growth

Answer 1

Lack of food, lack of shelter, disease, war, genocide, putting a limit to the amount of kids one may have, or how many can exist in a single generation.

Answer 2

So first of all, you might run out of food, which means that there wont be enough to sustain too many animals/people.
Or, you could simply run out of the space to have any more offspring. 
One final one is the introduction of a new predator, which would eat the population, making the growth unpredictable.

Hope this helped!!!! :D