EntityQ4392326· pop 5· linked from 21 articleshyperbolic growthSign in to savegrowth function exhibiting a singularity in a finite timeConnectionsmathematical singularityEntityInternational Standard Book NumberEntitygross domestic productEntityenzymeEntityWayback MachineEntityworld populationEntityhyperbolaEntityproportionalityEntitymathematical modelEntitymultiplicative inverseEntitylimit of a functionEntityMichael KremerEntityAndrey KorotayevEntitysubstrateEntitycarrying capacityEntityconvex functionEntityexponential growthEntitynonlinear systemEntityenzyme kineticsEntitypositive feedbackEntityCategoriesCurvesDifferential equationsMathematical analysisPopulationPopulation ecologySpecial functions