Instructions

Perform the following task and report them in accordance to the $$What to Submit$$ section:

$1.$ Modify the code below so that creates Figure $1$ exactly as it appears.

$2.$ Note that in this case K$=10$ and r$=0\mathrm{.}5.$

$3.$ The solution to the logistic equation P$=$ rP $(1-$P$/$K$)$ can be written as

PP$($tt$)=$ KKPP$0$eerrrr

KK $+$ PP$0($eerrrr $1)$

$4.$ State $($e$.$g$.,$ type$)$ the Logistic differential equation describing the dynamics of a Population $($P$)$ that

varies in time $($t$)$ with a growth rate $($r$)$ and carrying capacity $($K$).$ State its classification.

$5.$ The parts in the code that need to be changed are highlighted in yellow.

What To Submit

In MOER you will upload a pdf file and $.$m$$ MATLAB script. The report must include the following:

$$ A title with the name of the Project, followed by your first and last name and MEID.

$$ The recreated image with a caption.

$$ All MATLAB created figures can be easily copied and pasted in a Word document. Do not use

screenshots for this task! Every figure will need to have a label $($e$.$g$.,$ Figure $1)$ and a caption

explaining what is shown in the figure.

Page $|2$

Phoenix College Syllabus

$$ Upload the $.$m file that you created. The name that you need to use is $$First$\_$Last$\_$Slope$2.$m$.$ It

should be one file. The one when run produces the slope field and solution overlayed to it$.$

Figure $1$: This is the slope field for the given logistic equation that needs to be recreated exactly.

Rubric

Section Details Points

Image Matches the one given $80$

$.$m file The submitted file runs and recreates the

image $10$

Formatting$/$Reporting

Followed the assignment$$s requirements

with reporting needs, naming, and file

formats. $10$

Total $100$

Page $|3$

Phoenix College Syllabus

Code To Be Modified

$\%$ Code for Logistic Slope Field with Solutions.

r$=0\mathrm{.}5$; $\%$growth rate

K$=10$; $\%$Carrying capacity

t$=[0$:$0\mathrm{.}2$:$20]$; $\%$ vector for time

$\%$ Define the values of x and y that we will use to create the slope field

$\%$ We use tS and pS to identify the values of time and population

$\%$ to be used for slope field.

$[$tS$,$ pS$]=$ meshgrid$(\_\_\_\_\_\_\_\_)$;

$\%$ Define the values of the slope $($p$\text{'})$

s $=\_\_\_\_\_\_\_\_$;

$\%$ The following line is needed to find the size of each vector $(1,$s$)$ so

$\%$ that we can scale all of the arrows to have the same magnitude$=1$

L $=$ sqrt$(1+$ s$.^2)$;

figure$(2)$

hold on $\%$this command tell MATLAB to draw everything on the current figure

quiver$($tS$,$pS$,1./$L$,$s$./$L$,0\mathrm{.}5),$ axis tight

xlabel$(\text{'}$time$\text{'})$;

ylabel$(\text{'}$population$\text{'})$;

title$(\text{'}$Direction field for dp$/$dt $=$ r$*$p$*(1-$p$/$K$)\text{'})$;

$\%$ The nex part adds the solution curves to the slope field

$\%$ there are $3$ meaningful cases which we will draw in red, green, magenta

p$0=\_\_\_\_\_\_\_\_$;

p$=\_\_\_\_\_\_\_\_$;

plot$($t$,$p$,\text{'}$g$\text{'})$

p$0=$K;

p$=\_\_\_\_\_\_\_\_$;

plot$($t$,$p$,\text{'}$r$\text{'})$

p$0=5$;

p$=\_\_\_\_\_\_\_\_$;

plot$($t$,$p$,\text{'}$m$\text{'})$

hold off $\%$this command tell MATLAB to stop drawing on figureInstructions

Perform the following task and report them in accordance to the $$What to Submit$$ section:

$1.$ Modify the code below so that creates Figure $1$ exactly as it appears.

$2.$ Note that in this case K$=10$ and r$=0\mathrm{.}5.$

$3.$ The solution to the logistic equation P$=$ rP $(1-$P$/$K$)$ can be written as

PP$($tt$)=$ KKPP$0$eerrrr

KK $+$ PP$0($eerrrr $1)$

$4.$ State $($e$.$g$.,$ type$)$ the Logistic differential equation describing the dynamics of a Population $($P$)$ that

varies in time $($t$)$ with a growth rate $($r$)$ and carrying capacity $($K$).$ State its classification.

$5.$ The parts in the code that need to be changed are highlighted in yellow.

What To Submit

In MOER you will upload a pdf file and $.$m$$ MATLAB script. The report must include the following:

$$ A title with the name of the Project, followed by your first and last name and MEID.

$$ The recreated image with a caption.

$$ All MATLAB created figures can be easily copied and pasted in a Word document. Do not use

screenshots for this task! Every figure will need to have a label $($e$.$g$.,$ Figure $1)$ and a caption

explaining what is shown in the figure.

Page $|2$

Phoenix College Syllabus

$$ Upload the $.$m file that you created. The name that you need to use is $$First$\_$Last$\_$Slope$2.$m$.$ It

should be one file. The one when run produces the slope field and solution overlayed to it$.$

Figure $1$: This is the slope field for the given logistic equation that needs to be recreated exactly.

Rubric

Section Details Points

Image Matches the one given $80$

$.$m file The submitted file runs and recreates the

image $10$

Formatting$/$Reporting

Followed the assignment$$s requirements

with reporting needs, naming, and file

formats. $10$

Total $100$

Page $|3$

Phoenix College Syllabus

Code To Be Modified

$\%$ Code for Logistic Slope Field with Solutions.

r$=0\mathrm{.}5$; $\%$growth rate

K$=10$; $\%$Carrying capacity

t$=[0$:$0\mathrm{.}2$:$20]$; $\%$ vector for time

$\%$ Define the values of x and y that we will use to create the slope field

$\%$ We use tS and pS to identify the values of time and population

$\%$ to be used for slope field.

$[$tS$,$ pS$]=$ meshgrid$(\_\_\_\_\_\_\_\_)$;

$\%$ Define the values of the slope $($p$\text{'})$

s $=\_\_\_\_\_\_\_\_$;

$\%$ The following line is needed to find the size of each vector $(1,$s$)$ so

$\%$ that we can scale all o