That's true, but not really saying very much. Any differentiable function is locally linear around a neighborhood of any point where the derivative exists.
> Also exponential growth does hit some kind of ceiling relatively quickly.
Well... that depends. Much like how markets can remain irrational longer than you can remain solvent, exponential growth can often remain exponential for much longer than it takes to create a problem. Conversely, sometimes it can't remain exponential long enough to prevent a problem. Exponential growth is a hard beast to tame.