As always, a self contained ipynb solutions should be uploaded to Canvas along with a pdf copy. Each Question shall be clearly displayed inside the same notebook. Headers and formating will be graded
Use a modified Rickers Equation to answer the following questions about fish population.
$$ X_{n+1} = \Gamma(1,0.1) X_{n} e^{r_0(1-\frac{X_n}{K})} $$
where $\Gamma(1,0.1)$ is a noise variable with normal distribution centered at 1 and standard deviation of 0.1.
Each time step is another year
Until stated you can assume that $K=10000, r_0 =0.3$
Plot various(1000+) solutions on the same figure to illustrate how the noise can vary the solutions. You can assume that your starting fish population is 100 fish
After 5 years what range of fish would you expect to have if you started with
After 30 years, do you expect a larger distribution with higher growth rate or lower growth rate, you can assume $r_0 \in (0,1)$. Back this up with graphs and/or data.