No, that's not the shape of the line. You can view it here:
https://ourworldindata.org/grapher/global-average-gdp-per-ca...
The hockey stick upturn in recent centuries needs explanation.
I'm pushing back so hard on this comparative definition of wealth (which I notice is the secondary definition you found behind large possessions) because I think it's silly to do that when we have an unbelievably dramatic increase in wealth in recent centuries which needs understanding first.
Hand-waving away human progress and forcing zero sum definitions of wealth feels unserious. You have terms for things like inequality, why not use those instead of distorting what wealth means?