I was at a NASA workshop in Mountain View. An informational placard outside had two plots of growth, one with an unchecked exponential curve, and one with a curve that comes up to a peak and goes down. It asked which made more sense as a growth curve.
My idealized mathematical self thought, naturally, the exponential growth curve, because it expresses what happens when y-dot equals alpha y.
But I asked a passing Caltech astrophysicist, who (not surprisingly) gave a better reply. The curve that flattens out and goes down, he said, because exponential growth is impossible to sustain. Physical limits on some aspect of the system must intervene and impose a new law.
My idealized mathematical self thought, naturally, the exponential growth curve, because it expresses what happens when y-dot equals alpha y.
But I asked a passing Caltech astrophysicist, who (not surprisingly) gave a better reply. The curve that flattens out and goes down, he said, because exponential growth is impossible to sustain. Physical limits on some aspect of the system must intervene and impose a new law.