Problem $3$

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Create a script that projects population based on static:

Birth Rate $($BR$)$

Death Rate $($DR$)$

Calculate a migration that varies sinesoidally with time. Migration is given by the function $M(t)=$Mbase$+Mva{r}^{**}sin(2^{**}{p}^{**}\frac{t}{T}$per$),$ where Mbase is the base migration rate, Mvar is the variance in migration and Tper is the period in time over which it varies.

BR$,$ DR$,$ Mbase, Mvar, and Tper are provided at the start of the script template. The initial time $($tinit$),$ final time $($tfinal$),$ time step size $($delt$),$ and initial population $($Pinit$)$ are also provided. Please use $P$ for the population variable name and $M$ for the migration variable name. Create $P$ and $M$ as row vectors. Not following these conventions will result in an incorrect answer.

Once you have calculated $P,$ plot $P$ and $M$ as a functions of time on a $21$ subplot. Make sure to include axis labels and titles as this is good practice in plotting.

$BR=\mathrm{.}15$;

$DR=\mathrm{.}09$;

tinit $=0$;

tfinal $=100$;

delt $=\mathrm{.}5$;

Pinit $=400$;

Mbase $=0$;

Mvar $=2000$;

Tper $=10$;