There may be no upper bound on the absolute amount of available resources, but there is still a limit on how fast you can expand.
Consider the following maximal example: If all of Earth's resources are exhausted (whatever that means, I don't rely on any exact definition), we need to head outwards into space. Because our expansion is limited by the speed of light, we can at most cover a distance
r(t) = c * t
and thus a volume of space
V(t) = (c * t)^3
where t is the time spent travelling through space. The amount of available resources (assuming an even distribution of resources on the scale of the universe) is proportional to V, and thus to t^3.
Cubic growth is much much much much less than exponential growth. In fact, the exponential function can be shown to grow faster than any power function.
Consider the following maximal example: If all of Earth's resources are exhausted (whatever that means, I don't rely on any exact definition), we need to head outwards into space. Because our expansion is limited by the speed of light, we can at most cover a distance
and thus a volume of space where t is the time spent travelling through space. The amount of available resources (assuming an even distribution of resources on the scale of the universe) is proportional to V, and thus to t^3.Cubic growth is much much much much less than exponential growth. In fact, the exponential function can be shown to grow faster than any power function.