Suppose that a largemouth bass population $\backslash ($ P$($t$)\backslash )$ in a lake is attacked by a disease at time $\backslash ($ t$=0\backslash ),$ with the result that the fish cease to produce $($so that the birth rate is $\backslash (\backslash$beta$=0\backslash ))$ and the death rate $($deaths per week per fish$)$ is thereafter proportional to $\backslash (\backslash$frac$\{1\}\{\backslash$sqrt$\{$P$\}\}\backslash ).$ If there were initially $900$ bass in the lake and $256$ were left after $10$ weeks, how long did it take all the fish in the lake to die? Round your answer to two decimal places, if needed.

weeks