In a porous medium $($cross$-$sectional area $0\mathrm{.}5$ m$^2,$ length $1$ m$,$ porosity $0\mathrm{.}3),$ an aqueous polymer suspension is injected at a rate of $0\mathrm{.}0001$ m$^3/$s for unidirectional flow. If the viscosity of the suspension is $20$ x $10^3$ Pa$-$s$,$ and the permeability is related to cumulative flow invaded through the medium as k $($in darcy$)=(1-10$ Q$)$ where Q is in m$^3,$ what is the average permeability of the invaded zone when the fluid$-$suspension front is exactly halfway $($i$.$e$.,0\mathrm{.}5$ m from the inlet$).$