$p_{l+1}=p_l+r(1-p_l)p_l-h{p}_l.$

Problem $4[9$ points$]$: Your analysis in the previous question should have shown that all

equilibria are unstable if r $>$ h $+2.$ Use R to simulate your model and create a plot of the

population size $($as a fraction of the carrying capacity$)$ versus month $($see the Lab $2$ activity

for help$).$ Set h $=0\mathrm{.}3$ and simulate until time t $=5.$ Create three separate plots: one where

r is set so that p$=0$ is stable, one where r is set so that the non$-$zero equilibrium is stable,

and one where r $=3$ so that neither equilibrium is stable. Be sure to set appropriate axis

labels and set the title of each plot to be $$r $=$ xx$$ where $$xx$$ is the value you used for r

in creating that plot. You should save each plot as a separate pdf file and upload these files

with your submission on Crowdmark. To save plots in RStudio, click on the Zoom button in

the Plots panel and then right click and choose $$Save image as$...$ to save the plot to your

computer. Please also submit screenshots of the code used to create each of these plots.