It's almost certainly exponential, but the rate of growth depends on a number of dynamic factors. Corrupt elites often shut growth down. It happened in China and Japan several times in the second millennium, and it's happening in the US in the third one; we've backslid since about 1970.
Yeah so that's oncologists for one, suppose I go to Cuba to a real doctor the likes of which cannot be found in America and get treated for cancer. That's precisely what I want is for that doctor to shut the growth of the tumor down, be a corrupt elite to that tumor, tell it the show's over. It's part of my body like the runaway growth thing is part of the economy, but if either growth is harming its surrounding environment, taking up resources or pushing things out, forget it. Tumor repression, oppression and suppression, all three!
Exponential growth is too unstable, it can't go on forever. If it had taken place since before the Middle Ages, or any other dark age, like it would be too stupid everyone would either own or owe a galaxy. It's not just that's too much, it's also that would be a highly stupid premise for a life to be born into. So it's marketed like "hey we'd all be rich" but come on, for there to be credit there has to be debt, no creditors without debtors. In these fantasies they never talk about who'd be the debtor, but here's a hint, between the speaker talking about we are all going to be too rich for sins to matter, and the listeners, it's not the speaker.