[klyrs]

Assuming we need nothing but space to exist in, the surface area of the earth is finite. Expand that by a few km up and down, and humans still have a finite amount of space to live within.

If we're allowed colonization of space, we can only travel at a finite speed. Humans can overtake a finite radius in a year, resulting in a cubic rate of growth in volume. Exponential growth is ultimately limited by the finite speed of light and dimensionality of our universe.