Clear[a, b];
data = WolframAlpha["population of africa",
   {{"LongTermHistory:Population:CountryData", 1}, 
    "ComputableData"}];
gatheredData = {#[[1, 1]], Total[#[[All, 2]]]} & /@ 
   GatherBy[{#[[1, 1]], #[[2]]} & /@ Flatten[data, 1], First];
{a, b} = {a, b} /. 
   FindFit[{#[[1]] - 1600, #[[2]]} & /@ gatheredData, a*b^t, 
     {a, b}, t];
Labeled[Plot[a*b^(t - 1600), {t, 1600, 2010}, 
  Epilog -> Point[gatheredData],
  PlotRange -> All, Frame -> True, 
  GridLines -> {Range[1600, 2000, 100], {}},
  GridLinesStyle -> Directive[Thin, Opacity[0.2]],
  PlotStyle -> Thickness[0.008], ImageSize -> 444], Style[
    "Modelling the population of Africa with an exponential function",
  FontFamily -> "Times", FontSize -> 14] , Top]