Use MatLab Please. Do Question $5$ Please. In the case above, you may have been able to continually guess $$ values until you got close

enough to the solution, becanse the velocity depends fairly predictably on $.$ However, when

there are more parameters involved, it can be hard, if not imposible, to gucsis the parameters.

Let's return to the harvesting problem from last lab, which is

$\frac{dy}{dt}=\frac{a}{{10}^3}y(K-y)-$

for parameters $a($growth rate$),K($carrying capacity$),$ and $($harvesting rate$).$ The extra

${10}^3$ is a scaling factor to make the computations work out nicer. The

harvestingSolution method will take these three parameters, a value for $y(0)$ and a $T_f$ and

solve the harvesting problem from $0$ to $T_f.$ ssume that you measure the population of fish

in a lake $($estimating and taking an average of a few measurements$)$ and get, in thousands,

that the population over time is given in the table above.

Try two sets of parameters and compare the results to the data by drawing a plot of the

solution with those parameters and the data for each of the gucsses that you make. Do you

think you'd be able to guess what the parameters are for this situation?

Note: It is possible for the code to give you an error if the parameters are chosen poorly. If

this happens, try reducing the harvesting rate parameter $$ until it works. You'll also want

to be careful with the outputs from all of these functions when setting up your code.

tData $=[0,1,3,5,8,12,15,21]$;

yData $-50,64,104,142,174,186,188,188$;

$\%$ Guess some parameter's

figure$()$;

hold on;

plot$($tData$,$ yData, $\text{'}\text{'})$;

$\%$ Plot the solution for your choice of coefficients

hold off;

The function harvestingOptimization will find the optimum value of these constants from

the data given. Find these values, display them, and plot the solution with these parameters

alongside the data again.

figure$()$;

hold on;

plot$($tData$,$ yData, $\text{'}$ro$\text{'})$;

$\%$ Plot the optimal solution

hold off;