If we assume that when the population doubles the area it occupies is also doubled we can reason as follows: after n hours, there have been n/12 doublings, therefore we get an area of $P_n = 2^{n/12}\cdot 5\mathrm{mm}^2=\left(2^{1/12}\right)^n\cdot 5\mathrm{mm}^2\approx 1.0595^n\cdot 5\mathrm{mm}^2$.