Power-law growth of log-slope=2 is essentially a constant acceleration over time. For resource depletion, it's a fairly intuitive approach as one thinks of economic output in terms of a first-order linearly growing technology or a gradually growing population over time. When these are multiplicative the power can be greater than 2.

That's why I had originally considered this growth mode for resource depletion, as oil molecules don't act as exponential contagions -- they may provide some *autonomous* feedback in terms of self-accelerating technology growth but it's not as strong as the initially unconstrained positive autonomous feedback of virus contagion growth during an epidemic.