\[\frac{2.5}{2.0}=1.25\]
.In 2012 the world population was about 7 billion. After n generations the world population would be
\[7 \times 10^9 \times 1.25^n\]
.the Earth is roughly a sphere of
\[6370 km = 6.370 \times 10^6 m\]
so has a surface area equal to \[4 \pi r^2 = 4 \pi \times (6370 \times 10^6)^2 =5.1 \times 10^14 m^2\]
Over the whole surface of the Earth, each person will have only 1 square metre to call his own when the population equals the surface area.
\[7 \times 10^9 \times 1.25^n =5.1 \times 10^14 \]
This will be after
\[n = \frac{ln((5,1 \times 10^14)/(7 \times 10^9))}{ln 1.25} = 50\]
generations.If we take a generation as 45 years, there will be standing room only after
\[50 \times 45 = 2250\]
years.