A world population growth model: Interaction with Earth's carrying capacity and technology in limited space

• “Tamed quasi-hyperbolic function” fits world population growth over 1600 years.
• The form of this T-function is P(t) = A/[ln(B+e(D-t)/τ)]M.
• Population, Earth’s carrying capacity and technological skills interact.
• Space limitation may bring population explosion to a screeching halt by 2100.
• The best fit of model to data projects to a ceiling of 10.2 billion.

Up to 1900, world population growth over 1500 years fitted the quasi-hyperbolic format P(t) = a/(D − t)M, but this fit projected to infinite population around 2000. The recent slowdown has been fitted only by iteration of differential equations. This study fits the mean world population estimates from CE 400 to present with “tamed quasi-hyperbolic function” P(t) = A/[ln(B + e(D − t)/τ)]M, which reverts to P = a/(D − t)M when t <