Of course something totally unexpected could happen overnight (well, it did), but when you have several dozen economies most of which have been experiencing extremely rapid growth for many years now, and decades of trends towards reducing poverty across most of the continent, it is fairly reasonable to assume that the trends will continue for a while.

As it stands, they'd need to see a total catastrophic collapse of the economy of most of the African continent, with no subsequent recovery, for economic growth to not outpace population growth over the next few decades.

I think the past few years of economic growth in Africa had much to do with QE, and since QE stopped expanding, we have seen all EM economies suffer. I am not sure you can extrapolate this growth for the next 30 years.

Where do you get that idea from? Africa's growth has been going since ~2000, really taking off in 2003-2005. Nigeria's GDP grew by about 520 billion USD, or about 1000% from 2000 to 2014. In 2015 it was hurt somewhat by lower oil prices, but is still growing.

I'm sure you can't extrapolate it and assume it will stay the same for the next 30 years. But you can make reasonably educated estimates assuming that the average change in velocity will be all that extreme, given that large part of these amounts are based on income from relatively stable industries with well understood risk profiles.

Largely the development of Africa at present boils down to whether or not we see further major wars disrupt the progress. If we do, then, yes, things may go the wrong way. If not, it will take unprecedented crises to prevent Africa from continuing to see massive growth.