Why can't populations exponentially

Populations must grow gradually, people can't just suddenly reproduce a substancial amount.

One of the reasons that an population cant grow exponentially is because there is a certain capacity that each environment has and once that capacity is reached it cannot go above it. If the population does happen to go over that limit it will have to decrease again because the amount of supplies, the availability of shelter and even the number of mates that are available are limited. Without these items the population cannot grow.

hope this helps :)