wow i didnt see this coming, but i have NO idea how to do this webassign

anyhelp would be greatly appreciate - let me know if you can help me out

For each of the following models you will be using these parameter values: M = 106100, r = 0.2981, and H = 3953. Please note k=r/M.
For the exponential model, if the initial population ( y(0) ) is 1345,


(Symbolic) write the equation for y in terms of t
Note: Use ONLY the variable t. If you need to denote "e" remember to use the "exp" format (just like in Excel!).
y (t) =


what is the population at t=15?




For the logistic model,


what is the population at the nonzero equilibrium?



If y(0) = 1345, what is the population at t=15?




For the harvesting model,


what are the equilibrium populations?
(smaller population)
(larger population)



Use Maple to create two graphs of the harvesting model solution using DEplot for y(0) = 31628 and y(0) = 7768, for t = 0 to t = 10.

3/21/2006 11:32:46 PM

if you think you can do this - i can link the class notes which suck 99.9% of the time -

thanks again in advance

3/21/2006 11:34:09 PM

Not that this will really help, because I don't remember how to do it, but if you go to class every time, she does the exact homework assignment with different numbers. the only way you can make an A (unless you are a genious or know someone that understands this stuff) is to try and get it done during class so she can help you.

I went a little early and filled out the spreadsheets ahead of time so when she zipped through the problems I could easily plug in the numbers and solve.

Not trying to be negative...just telling you my experience with the class.

3/22/2006 1:20:35 PM

I dont have a "she" I have a "he" and he doesn't teach very well, especially at 8am

3/22/2006 1:24:36 PM

#1 - i have gone to 1 class and masterD is right - 8 am doesnt work
#2 - i have a great girlfriend/friends to help me with this crap
#3 - this class is pointless
#4 - repeat step 3
#5- repeat step 4
#6 - for some reason this is the ONLY webassign left i cant do, nor anyone i know - i know there are some ridiculous smart people on here, so id figure id give it a shot

3/22/2006 1:45:50 PM

I'll help you out with some Maple, maybe this will get you started.

use the following command to add DEtools
> with(DEtools):

Now if I wanted to solve d/dt{P(t)}= k*(M-P(t))*P(t)

I would use the following to define the ODE
>ode1:=diff(P(t),t)=k*(M-P(t))*P(t); <---- This is the logistic DE you want

Then to DEplot use
>DEplot(ode1,P(t),t=0..10,[[P(0)=7768]],P=0..100000);

The arguments of DEplot are
1. the ODE
2. What you are solving for.. in this case P(t)
3. the time scale
4.the Initial condition notice the brackets.
5. The scale for the P-axis.

If you want to solve a ODE use
>dsolve(...)

If you need help with dsolve

type

>?dsolve

BUt you should be able to find a formula for the soln of the logistic DE. It's pretty standard.


[Edited on March 22, 2006 at 2:01 PM. Reason : .nvmnd]

3/22/2006 1:52:54 PM

ok, so i did it in class and dont have my notes with me at work

however i pulled up the maple file i submitted, and although it doest make much sense, it does have some of the equations i used.

see if you can figure it out

btw, it doesnt have the logistic...just the exponential and harvest

Quote :

"<?xml version="1.0" encoding="UTF-8" ?> - <Worksheet> <Version major="6" minor="1" /> - <View-Properties> <Zoom percentage="100" /> </View-Properties> - <Styles> <Layout alignment="left" bullet="none" name="Warning" /> <Layout alignment="left" bullet="none" firstindent="0.0" leftmargin="0.0" linebreak="space" linespacing="0.0" name="Normal" rightmargin="0.0" spaceabove="0.0" spacebelow="0.0" /> <Layout alignment="centred" bullet="none" name="Maple Plot" /> <Layout alignment="centred" bullet="none" linespacing="0.5" name="Maple Output" /> <Font background="[0,0,0]" bold="true" executable="true" family="Monospaced" foreground="[255,0,0]" name="Maple Input" opaque="false" size="12" /> <Font background="[0,0,0]" family="Monospaced" foreground="[0,0,255]" name="Warning" opaque="false" readonly="true" size="12" /> <Font background="[0,0,0]" family="Times New Roman" foreground="[0,0,255]" name="2D Output" opaque="false" readonly="true" size="12" /> </Styles> - <Group> - <Input> <Text-field layout="Normal" prompt=">" style="Maple Input">with(plots):</Text-field> </Input> - <Output> <Text-field layout="Warning" style="Warning">Warning, the name changecoords has been redefined</Text-field> </Output> </Group> - <Group> - <Input> <Text-field layout="Normal" prompt=">" style="Maple Input">with(DEtools):</Text-field> </Input> </Group> - <Group> - <Input> <Text-field layout="Normal" prompt=">" style="Maple Input">exponential:=diff(y(t),t)=r*y(t);</Text-field> </Input> - <Output> - <Text-field layout="Maple Output" style="2D Output"> <Equation>NiM+SSxleHBvbmVudGlhbEc2Ii8tSSVkaWZmR0kqcHJvdGVjdGVkR0YpNiQtSSJ5R0YlNiNJInRHRiVGLiomSSJyR0YlIiIiRitGMQ==</Equation> </Text-field> </Output> </Group> - <Group> - <Input> <Text-field layout="Normal" prompt=">" style="Maple Input">expsol:=dsolve({exponential,y(0)=y0},y(t));</Text-field> </Input> - <Output> - <Text-field layout="Maple Output" style="2D Output"> <Equation>NiM+SSdleHBzb2xHNiIvLUkieUdGJTYjSSJ0R0YlKiZJI3kwR0YlIiIiLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRjFJKF9zeXNsaWJHRiU2IyomSSJyR0YlRi1GKkYtRi0=</Equation> </Text-field> </Output> </Group> - <Group> - <Input> <Text-field layout="Normal" prompt=">" style="Maple Input">expsol2:=subs(r=.2735,y0=1345,expsol);</Text-field> </Input> - <Output> - <Text-field layout="Maple Output" style="2D Output"> <Equation>NiM+SShleHBzb2wyRzYiLy1JInlHRiU2I0kidEdGJSwkLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRi9JKF9zeXNsaWJHRiU2IywkRiokIiVORiEiJSIlWDg=</Equation> </Text-field> </Output> </Group> - <Group> - <Input> <Text-field layout="Normal" prompt=">" style="Maple Input">expsol3:=t->1345*exp(.2735*t);</Text-field> </Input> - <Output> - <Text-field layout="Maple Output" style="2D Output"> <Equation>NiM+SShleHBzb2wzRzYiZio2I0kidEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCQtSSRleHBHNiRJKnByb3RlY3RlZEdGMEkoX3N5c2xpYkdGJTYjKiYkIiVORiEiJSIiIjkkRjciJVg4RiVGJUYl</Equation> </Text-field> </Output> </Group> - <Group> - <Input> <Text-field layout="Normal" prompt=">" style="Maple Input">expsol3(15);</Text-field> </Input> - <Output> - <Text-field layout="Maple Output" style="2D Output"> <Equation>NiMkIisoWyQzTyIpISIm</Equation> </Text-field> </Output> </Group> - <Group> - <Input> <Text-field layout="Normal" prompt=">" style="Maple Input">harvest:=diff(y(t),t)=r*(1-y(t)/M)*y(t)-H;</Text-field> </Input> - <Output> - <Text-field layout="Maple Output" style="2D Output"> <Equation>NiM+SShoYXJ2ZXN0RzYiLy1JJWRpZmZHSSpwcm90ZWN0ZWRHRik2JC1JInlHRiU2I0kidEdGJUYuLCYqKEkickdGJSIiIiwmRjJGMiomRitGMkkiTUdGJSEiIkY2RjJGK0YyRjJJIkhHRiVGNg==</Equation> </Text-field> </Output> </Group> - <Group> - <Input> <Text-field layout="Normal" prompt=">" style="Maple Input">harvestsol:=dsolve({harvest,y(0)=y0},y(t));</Text-field> </Input> - <Output> - <Text-field layout="Maple Output" style="2D Output"> <Equation>NiM+SStoYXJ2ZXN0c29sRzYiLy1JInlHRiU2I0kidEdGJSwkKiYsJiomSSJyR0YlIiIiSSJNR0YlRjBGMComLUkldGFuaEc2JEkqcHJvdGVjdGVkR0Y2SShfc3lzbGliR0YlNiMsJComLCYqJkYqRjAsJiooSSJIR0YlRjBGMUYwRi9GMCEiJSomRi8iIiNGMUZCRjAjRjBGQiEiIiomRjFGMC1JKGFyY3RhbmhHRjU2IyooRi9GMCwmSSN5MEdGJSEiI0YxRjBGMEY9I0ZERkJGMEZCRjBGMUZERkNGMEY9RkNGREYwRi9GREZD</Equation> </Text-field> </Output> </Group> - <Group> - <Input> <Text-field layout="Normal" prompt=">" style="Maple Input">harvestsol2:=subs(r=.2735,M=114800,H=3924,Y0=1345,harvestsol);</Text-field> </Input> - <Output> - <Text-field layout="Maple Output" style="2D Output"> <Equation>NiM+SSxoYXJ2ZXN0c29sMkc2Ii8tSSJ5R0YlNiNJInRHRiUsJiQiKysrK1NkISImIiIiLUkldGFuaEc2JEkqcHJvdGVjdGVkR0YzSShfc3lzbGliR0YlNiMsJkYqJCErOiR5MG4qISM2LUkoYXJjdGFuaEdGMjYjLCZJI3kwR0YlJCEraSJmTlkjISM5JCIrZkgzOTkhIipGL0YvJCErIXpuImZTRi4=</Equation> </Text-field> </Output> </Group> - <Group> - <Input> <Text-field layout="Normal" prompt=">" style="Maple Input">numharvestsol:=subs(r=.2735,M=114800,H=3924,harvest);</Text-field> </Input> - <Output> - <Text-field layout="Maple Output" style="2D Output"> <Equation>NiM+SS5udW1oYXJ2ZXN0c29sRzYiLy1JJWRpZmZHSSpwcm90ZWN0ZWRHRik2JC1JInlHRiU2I0kidEdGJUYuLCYqJiwmIiIiRjJGKyMhIiIiJytbNkYyRitGMiQiJU5GISIlISVDUkYy</Equation> </Text-field> </Output> </Group> - <Group> - <Input> <Text-field layout="Normal" prompt=">" style="Maple Input">rhs(numharvestsol);</Text-field> </Input> - <Output> - <Text-field layout="Maple Output" style="2D Output"> <Equation>NiMsJiomLCYiIiJGJi1JInlHNiI2I0kidEdGKSMhIiIiJytbNkYmRidGJiQiJU5GISIlISVDUkYm</Equation> </Text-field> </Output> </Group> - <Group> - <Input> <Text-field layout="Normal" prompt=">" style="Maple Input">solve(%,y(t));</Text-field> </Input> - <Output> - <Text-field layout="Maple Output" style="2D Output"> <Equation>NiQkIis1QSQzbyIhIiYkIishem4iKnoqRiU=</Equation> </Text-field> </Output> </Group> - <Group> - <Input> <Text-field layout="Normal" prompt=">" style="Maple Input">DEplot(numharvestsol,y(t),t=0...10,[[y(0)=31398]],'arrows'='NONE');</Text-field> </Input> - <Output> - <Text-field layout="Maple Plot"> <Plot height="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" type="two-dimensional" width="400">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</Plot> </Text-field> </Output> </Group> - <Group> - <Input> <Text-field layout="Normal" prompt=">" style="Maple Input">DEplot(numharvestsol,y(t),t=0...10,[[y(0)=8404]],'arrows'='NONE');</Text-field> </Input> - <Output> - <Text-field layout="Maple Plot"> <Plot height="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" type="two-dimensional" width="400">LSUlUExPVEc2Ji0lJ0NVUlZFU0c2JTc3NyQkIiIhRiskIiUvJSlGKzckJCIrKysrK10hIzUkIjM4XnlhNFNKX3UhIzk3JCQiKysrKys1ISIqJCIzciMqUj9FdEohUSdGNDckJCIrKysrKzpGOCQiM0lkLVhTUXFwXkY0NyQkIisrKysrP0Y4JCIzOSFvXVx2KWUpeiRGNDckJCIrKysrK0RGOCQiMyEpXF1DRmVmU0FGNDckJCIrKysrK0lGOCQiM2k0a1VQW1tPWSEjOjckJCIrKysrK05GOCQhM0VAPiskKVFscjpGNDckJCIrKysrK1NGOCQhM0YsaXV2MkQ5UkY0NyQkIisrKysrWEY4JCEzbnojZXE5JXBEbUY0NyQkRjBGOCQhMyhHRjZwMydcJXkqRjQ3JCQiKysrKytiRjgkITMyYkEzIUdUI1w4ISM4NyQkIisrKysrZ0Y4JCEzRV0+SXpeUCl5IkZibzckJCIrKysrK2xGOCQhM0NQLDg7WiZSSiNGYm83JCQiKysrKytxRjgkITMuX1EhW3QmKTQmSEZibzckJCIrKysrK3ZGOCQhM0I/X0JJKT1ddCRGYm83JCQiKysrKyshKUY4JCEzTD0vTk04UD1aRmJvNyQkIisrKysrJilGOCQhMz4pXEFEZlg4KWZGYm83JCQiKysrKyshKkY4JCEzWnotPlVuJVFsKEZibzckJCIrKysrKyYqRjgkITNtdGxwXyYqcGcqKkZibzckJEY3ISIpJCEzJUdNamBsdEZMIiEjNy0lJlNUWUxFRzYjJSVMSU5FRy0lKlRISUNLTkVTU0c2IyIiJC0lK0FYRVNMQUJFTFNHNiRRInQ2IlEleSh0KUZdcy0lJVZJRVdHNiQ7JCEiJiEiIiQiJDAiRmVzOyQhK1FWaC45ISIlJCIrR28hKVs6RmRzLSUmQ09MT1JHNiYlJFJHQkckIjEjPXQ6IXpnPiEqISM7RmJ0JCIyQ0stKUgrKys/ISM8</Plot> </Text-field> </Output> </Group> - <Group> - <Input> <Text-field layout="Normal" prompt=">" style="Maple Input" /> </Input> </Group> <Text-field /> </Worksheet>"

lemme help you further...to start the exponential use

with(plots)
with(DEtools)
exponential:=diff(y(t),t)=r*y(t);


....as you can see, all the info is in there...finding it is a different story...



[Edited on March 22, 2006 at 1:59 PM. Reason : ]

3/22/2006 1:56:49 PM

thank you guys so much

3/22/2006 5:52:01 PM

i only need the logistic model part now - the rest i got

what is the population at the nonzero equilibrium?



If y(0) = 1345, what is the population at t=15?



any ideas?

3/22/2006 11:04:56 PM

yea this is the problem i have

i got all the rest

but the logistical is coming up wrong

3/22/2006 11:06:40 PM

ok Sipn - the first part of logistic is the M value





if anyone can help me with If y(0) = 1345, what is the population at t=15? i would be very thankful

3/22/2006 11:17:19 PM

Quote :

"what is the population at the nonzero equilibrium?"

Its whatever the "M" value is.

Quote :

"If y(0) = 1345, what is the population at t=15?"

If you have Maple, then input this command into it:

dsolve({diff(y(t),t)=0.2765/116600*(116600-y(t))*y(t),y(0)=1480});

(In my problem, 0.2765 = r and 116600 = M)

You should get a formula that you can plug "t" into and get the population for.

[Edited on March 22, 2006 at 11:20 PM. Reason : Clarification]

3/22/2006 11:17:57 PM

The nonzero equilbrium for the logistic model is called the carrying capcacity. I can find how you
guys write the model ( there are several possibilities ) but

"M = 106100, r = 0.2981, and H = 3953" ...

If I had to guess I'd say the answer is either 106100 or 3953.

3/22/2006 11:20:37 PM

Quote :

"i only need the logistic model part now - the rest i got what is the population at the nonzero equilibrium? If y(0) = 1345, what is the population at t=15?"

Did you totally ignore my post or what? I practically gave you the answer. Kids these days

> M:=106100;



> r:=0.2981;



> H=3953;



> k:=r/M;


> ode1:=diff(P(t),t)=k*(M-P(t))*P(t);


> DEplot(ode1,P(t),t=0..30,[[P(0)=7768]],P=-10..120000);
>

> soln(t):=(simplify(dsolve({ode1,P(0)=1345},P(t))));


> evalf(limit(soln(t),t=infinity));

lim P(t) = 106100. <--------- Here's what you want ...
t -> infinity


[Edited on March 22, 2006 at 11:51 PM. Reason : cleaned up output]

[Edited on March 22, 2006 at 11:52 PM. Reason : .<--------]

3/22/2006 11:47:53 PM

lol my bad i skipped it and just put in the maple deal

i got em all anyway - thanks guys

3/22/2006 11:59:29 PM