Continuing, with $\backslash ($ N$=$x$+$y $\backslash )$ a constant, and that $\backslash ($ x$=\backslash )$ the number of zombies and $\backslash ($ y$=\backslash )$ the numbers of normal humans at time $\backslash ($ t $\backslash )$ in days, and the model of the rate of change of the numbers of zombies to be $\backslash (\backslash$frac$\{$d x$\}\{$d t$\}=$k x y $\backslash ).$

Say on day zero $(\backslash ($ t$=0\backslash )),$ there is initially one zombie. By day $10(\backslash ($ t$=10\backslash )),$ there is $100$ zombies.

If on this island there is a total of $\backslash ($ N$=1\backslash )$ million beings, by what day will half the population on the island be zombies?

$($Round your answer to $4$ decimal places$).$

Hint. To solve this you should again put everything in terms of $\backslash ($ x $\backslash )$ and $\backslash ($ t $\backslash ).$ This is in fact a Bernoulli differential equation, however you do not need the method $($of substitution$)$ for Bernoulli to solve this DE$,$ as you have already identified in the previous part what kind this is $($you could treat it as Bernoulli however, both ways work!$).$ Using the relevant integration technique, you can solve for a $1$parameter family of solutions $\backslash ($ x$=$x$($t$)\backslash ),$ Using the information given, you can determine all the unknown coefficient and parameters.