dcc + differential equations = atrocious

[phagist_]

well, do you have any specific problems in mind?

[dusty_girl1144]

well, do you have any specific problems in mind?

A colony of seals is declining in numbers so that there are "N" seals at the time "t" years. it is assumed that the rate of decline is proportional to  "N". initially in the period of study there were 5000 seals in the colony but after 5 years, a 5% decline was noted. set up the differential equation and solve it, expressing "N" in terms of "t"

* wen it says proportional. am i right in saying:
dN/dt = -kN? where k is a constant?, and the -ve coz its a decline?

after this im stuck only because of the 5% thingy thanxs heaps!

[phagist_]

yep so you have


you are given (when ) and using the 5% decline information you can get another set of data points (when ).

You need both sets since you need to find the constant of integration and the constant of proportionality
So;



and

[bigtick]

Another question
Is ?

[Mao]

Another question
Is ?

at first glance it doesn't look like it's right,
but at the time this question popped up, someone did assure me it was basically just the chain rule, and I did somehow manage to convince myself with some reasoning or other

so to be quite frank, I don't have a clue right now

[bigtick]

Try with .

[Mao]

Try with .

i see what you mean.

[dusty_girl1144]

yep so you have


you are given (when ) and using the 5% decline information you can get another set of data points (when ).

You need both sets since you need to find the constant of integration and the constant of proportionality
So;



and

i dont exactly get how u just pluged numbers in. lol.
like where does the intergration and the flip of dN/dt come in? 


  lol

[Mao]

well, do you have any specific problems in mind?

A colony of seals is declining in numbers so that there are "N" seals at the time "t" years. it is assumed that the rate of decline is proportional to  "N". initially in the period of study there were 5000 seals in the colony but after 5 years, a 5% decline was noted. set up the differential equation and solve it, expressing "N" in terms of "t"

* wen it says proportional. am i right in saying:
dN/dt = -kN? where k is a constant?, and the -ve coz its a decline?

after this im stuck only because of the 5% thingy thanxs heaps!

firstly:

"it is assumed that the rate of decline is proportional to  "N""
that is, rate of change of population is negative (decline) and is proportional to N









at t=0, N=5000



at t=5, N has dropped 5%



solving these two simultaneously will give the values for k and c, which you can then just sub in and rearrange

[dusty_girl1144]

well, do you have any specific problems in mind?

A colony of seals is declining in numbers so that there are "N" seals at the time "t" years. it is assumed that the rate of decline is proportional to  "N". initially in the period of study there were 5000 seals in the colony but after 5 years, a 5% decline was noted. set up the differential equation and solve it, expressing "N" in terms of "t"

* wen it says proportional. am i right in saying:
dN/dt = -kN? where k is a constant?, and the -ve coz its a decline?

after this im stuck only because of the 5% thingy thanxs heaps!

firstly:

"it is assumed that the rate of decline is proportional to  "N""
that is, rate of change of population is negative (decline) and is proportional to N

is that the same as dN/dt = -kN? (like without the fishy sign?)

if it is. yeah ive gotten that so far. whats next?

[Mao]

[i do a lot of edits, that was a mistake i made in copy-pasta]

[dusty_girl1144]

well, do you have any specific problems in mind?

A colony of seals is declining in numbers so that there are "N" seals at the time "t" years. it is assumed that the rate of decline is proportional to  "N". initially in the period of study there were 5000 seals in the colony but after 5 years, a 5% decline was noted. set up the differential equation and solve it, expressing "N" in terms of "t"

* wen it says proportional. am i right in saying:
dN/dt = -kN? where k is a constant?, and the -ve coz its a decline?

after this im stuck only because of the 5% thingy thanxs heaps!

firstly:

"it is assumed that the rate of decline is proportional to  "N""
that is, rate of change of population is negative (decline) and is proportional to N









at t=0, N=5000



at t=5, N has dropped 5%



solving these two simultaneously will give the values for k and c, which you can then just sub in and rearrange

ok i get it up to t=0, N=5000.
but after that im kinda lost on how u get 3 on the last line
and like is something cut out after the 100? lol :s

[*Roxxii*]

is that the same as dN/dt = -kN? (like without the fishy sign?)

if it is. yeah ive gotten that so far. whats next?

ROFL @ "fishy sign" !! hehee 

[Mao]

ok i get it up to t=0, N=5000.
but after that im kinda lost on how u get 3 on the last line
and like is something cut out after the 100? lol :s

yeah, it didn't like my % sign. fixed now.

[dusty_girl1144]

[/tex][/tex]

well, do you have any specific problems in mind?

A colony of seals is declining in numbers so that there are "N" seals at the time "t" years. it is assumed that the rate of decline is proportional to  "N". initially in the period of study there were 5000 seals in the colony but after 5 years, a 5% decline was noted. set up the differential equation and solve it, expressing "N" in terms of "t"

* wen it says proportional. am i right in saying:
dN/dt = -kN? where k is a constant?, and the -ve coz its a decline?

after this im stuck only because of the 5% thingy thanxs heaps!

firstly:

"it is assumed that the rate of decline is proportional to  "N""
that is, rate of change of population is negative (decline) and is proportional to N









at t=0, N=5000



at t=5, N has dropped 5%



solving these two simultaneously will give the values for k and c, which you can then just sub in and rearrange

hummm ok. well so far my 2 simultaneous equations are

5=-1/k ln(4750)+ C
0=-1/k


it works out to be 5= -1/k ln(4750) + 1/k ln(5000)
therefore equals 5 = 1/k (ln(5000)/(4750)) ==> 5=1/k(ln(20/29))

k = 1/5 (ln(20/19))


subbed back in i get. 0= -5/ln(20/19) x ln(5000) + C

therefore C = 5(ln(5000))/ln(20/19)

..... t = -5/ln (20/19) X Ln (N) + 5(ln(5000))/ln(20/19)


am i CLOSE to correct? if so i sub t and find N? t=5?


btw how do u do the itergration sign and the devision things. coz my post looks like shit! lol