A natural population growth, without predation or starvation, would be geometric, i.e. doubles every given time period. Predation (comsumption for food by other species) or starvation (lack of food supply) limits this growth so that no one species overwhelms its environment.
Human population does not follow a natural growth pattern, as we have the ability to shape our environment to fit, we protect ourselves from predators, we produce our food rather than having to find it lying around somewhere, and we can fix things that might go wrong with us. Thus our population growth becomes closer to exponential rather than geometric.
I've read that half the people who have EVER been alive on Earth, for the entirety of human history, are living at this very moment. In other words, only 1 of every 2 people who have ever lived have actually died!