Comment by zomglings

Very good point.

One thing to add - in my experience, you need to spend money to go from merely superlinear to (locally) exponential.

This is the original reason that VCs exist.

If you go to an intelligent decisionmaker at a VC firm with proof of sustained superlinear growth and plan for how their capital will allow you to increase the rate (and higher derivatives) of your growth, they will almost certainly invest.

The reason that VCs have to specialize by industry or look for signals like Stanford/Harvard/whatever is that it's very difficult to validate or invalidate proof of superlinear growth. This requires specialization or, if lazy, social signals like the university you graduated from.