Going to space still cannot outrun an exponential function. Extrapolating exponential growth always leads to catastrophe. Imagine the sphere of a civilization

Going to space still cannot outrun an exponential function. Extrapolating exponential growth always leads to catastrophe. Imagine the sphere of a civilization expanding in space at some speed, in all directions. The volume of this sphere would equal time cubed (t^3) times some constant. Now suppose this civilization has a magical power source that allows them to keep growing power consumption exponentially. So power consumption would equal 2^t (where time unit = one doubling time, 35 years in the case of 2% growth) times some constant. 2^t will always overtake t^3 no matter the constants, so power density of the sphere trends to infinity, so the civilization will cook itself in waste heat.