Practice DE Modeling for Rhinoceros Population

[Redbelly98]

Well, you have a quadratic expression in P: {P}({\frac{P}{g}-1}) = P^2/g - P. That's solvable, but kinda messy, so-o-o-o...

... before we go solving for P, I recommend confirming whether it satisfies the differential equation first. (If it doesn't, then there's no need to spend time on solving for P ) So, implicit differentiation and c e^{rt} = {P}({\frac{P}{g}-1}) ...

 

[I like Serena]

OK so it is good I took a break from this lol. I just did it in 30 mins and I have a solution...which may not be the correct solution but it is a solution. I want to try LaTex, but I think it would be easier for me to just take a pic of my work and post it lol. I got ce^rt/[(P/g)-1]=P? If this is it I can understand why you were saying it is surprising lol I did all of these algebraic gymnastics and looked down on my paper and saw P((P/g)-1) again lol.

btw I was working on the model I came up with, not the "correcter" one

I'm glad you decided to stay and solve it. :)

But I don't understand how you got to your solution.
What did you do to arrive at it?

 

[HeLiXe]

Yes ILS I thought you were losing faith in me

I solved it analytically by separation of variables. I think I will just post a picture of the paper I worked on...well...I will rewrite it and post it because that paper is a bit wild. And it is ce^kt not rt...we were working with r as a constant on my last DE exam and I arbitrarily posted it here.

 

[HeLiXe]

Well, you have a quadratic expression in P: {P}({\frac{P}{g}-1}) = P^2/g - P. That's solvable, but kinda messy, so-o-o-o...

... before we go solving for P, I recommend confirming whether it satisfies the differential equation first. (If it doesn't, then there's no need to spend time on solving for P ) So, implicit differentiation and c e^{rt} = {P}({\frac{P}{g}-1}) ...

Ok redbelly...I think I see where you are going with this. I am still foggy about DE because we are just solving everything in class, but I am not really understanding the application of them or why they are being used (which is why I started the modeling practice). So I could be missing some fundamental things and I appreciate if anyone points them out to me!

I will post my work for this solution.

 

[HeLiXe]

Well in writing it over I noticed that I made a mistake when I was doing the partial fraction decomposition..."A" was supposed to = -1 and I wrote it as 1 when I was putting the value of A in place of A, so that changes the answer to

{\frac{\frac{P}{g}-1}{P}} = c e^{kt}

Here is my work
[PLAIN]http://img810.imageshack.us/img810/4249/rhincalc.png
the "g" got cut off at the bottom there :D

 

[Redbelly98]

Well in writing it over I noticed that I made a mistake when I was doing the partial fraction decomposition..."A" was supposed to = -1 and I wrote it as 1 when I was putting the value of A in place of A, so that changes the answer to

{\frac{\frac{P}{g}-1}{P}} = c e^{kt}

And the best part is, that can be solved for P explicitly, no sweat

(And then you can get dP/dt, and confirm whether the original differential equation is satisfied)

 

[HeLiXe]

cool

 

[I like Serena]

Well in writing it over I noticed that I made a mistake when I was doing the partial fraction decomposition..."A" was supposed to = -1 and I wrote it as 1 when I was putting the value of A in place of A, so that changes the answer to

{\frac{\frac{P}{g}-1}{P}} = c e^{kt}

Very good!

Sorry I tried to get you to do the simpler case.
Apparently that would have been no challenge at all!

But, uhh, what is P explicitly?

And I want a picture!

 

[HeLiXe]

Very good!

Sorry I tried to get you to do the simpler case.
Apparently that would have been no challenge at all!

I think it would have been for me -_- The things others usually refer to as "simple" are usually very complicated for me lol

But, uhh, what is P explicitly?

And I want a picture!

Is not the picture of my work good enough??
I have some errands to run and stuff but when I get a chance I will do the explicit thing and post a picture of it

 

[I like Serena]

I think it would have been for me -_- The things others usually refer to as "simple" are usually very complicated for me lol

Aaaah, so that's what the remark about the S-word was about!
So S-problems are more of a challenge for you?

Is not the picture of my work good enough??
I have some errands to run and stuff but when I get a chance I will do the explicit thing and post a picture of it

Well... errr... yes... the picture of your work was quite good... but... I can only say..

More! More! More!

 

[HeLiXe]

Btw, will you let us know how your chem test went?

Hi ILS
Just wanted to let you know I finally got my grades back in for my chem exams and I got A's on all of them (including the final). I missed one question on each one grrrr.

Aaaah, so that's what the remark about the S-word was about!
So S-problems are more of a challenge for you?

unfortunately yes -_- and it leads many to think I am terribly stupid lol

Well... errr... yes... the picture of your work was quite good... but... I can only say..

More! More! More!

OK starting it now...I hope we're still friends That night when I got back the chem teacher sent out an e-mail about an extra credit assignment and so I got to that right away...and lately my brain can only handle one of the "heavy things" at a time. I hope that gets better soon -_-

I also might be asking some questions about eigenvectors and the trace coordinate plane for 2 dimensions...I think I'm following the 3-D stuff, but the 2-D stuff is a little confusing with the saddles and spirals and all of this stuff on the same graph as a parabola...and a line or something I have no idea what's going on...I cannot visualize what my prof is trying to convey.

 

[I like Serena]

Hi ILS
Just wanted to let you know I finally got my grades back in for my chem exams and I got A's on all of them (including the final). I missed one question on each one grrrr.

Congratulations!

OK starting it now...I hope we're still friends That night when I got back the chem teacher sent out an e-mail about an extra credit assignment and so I got to that right away...and lately my brain can only handle one of the "heavy things" at a time. I hope that gets better soon -_-

I also might be asking some questions about eigenvectors and the trace coordinate plane for 2 dimensions...I think I'm following the 3-D stuff, but the 2-D stuff is a little confusing with the saddles and spirals and all of this stuff on the same graph as a parabola...and a line or something I have no idea what's going on...I cannot visualize what my prof is trying to convey.

Oh, friendship does not depend on doing homework or not.

Perhaps I'll be able to confuse you some more with eigenvectors, saddles, spirals, and stuff like that!

 

[HeLiXe]

Congratulations!

Thank you!

Oh, friendship does not depend on doing homework or not.

Perhaps I'll be able to confuse you some more with eigenvectors, saddles, spirals, and stuff like that!

Yes you will see some stuff from me in the near future. And my chem class is ended I am just waiting on the final grade.

I got g(1-g)/ce^kt = P...I was trying to put it in laTex but could not get the t to stay in the denominator as an exponent. I am working on the derivative now.

 

[I like Serena]

I got g(1-g)/ce^kt = P...I was trying to put it in laTex but could not get the t to stay in the denominator as an exponent. I am working on the derivative now.

Did you try to use curly thingies in LaTeX?
That's what is used to group stuff together.

 

[HeLiXe]

I did this
{\frac{g(1-g)}{c e^{kt}}} = P

 

[HeLiXe]

-_- ok it seems it worked lol

 

[I like Serena]

Good!

 

[I like Serena]

Did you finish the derivative?
And did it match the DE?

 

[HeLiXe]

Yes but I need to recheck it. It matched ... but I still wonder if I made an error lol.

 

[I like Serena]

Show your work?
I got a different solution...
(Perhaps I made a mistake! )

 

[Redbelly98]

I get a different solution too.

 

[HeLiXe]

Show your work?
I got a different solution...
(Perhaps I made a mistake! )

>_> I ^highly doubt you made a mistake. I will post my work a little later... right now I think I will start something on eigenvectors and the trace determinant plane as I have an exam on it tomorrow.

I get a different solution too.

Yikes! This means my calculus skills are just as bad as my DE skills -_- or maybe it's my algebra lol. I will post what I did later.

 

[I like Serena]

>_> I ^highly doubt you made a mistake. I will post my work a little later... right now I think I will start something on eigenvectors and the trace determinant plane as I have an exam on it tomorrow.

I'm only a _lowly practitioner of science... and does that mean you'll be starting new threads? :)

 

[HeLiXe]

lol yes hopefully -_- I'm really happy that you guys are so patient with me. I'm having a really rough time this semester.