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Differential equation

iam not able to solve Q 12.
I solved the diff eq and got 1/100[ln(P/100-P)=Kt/100+C15961171999881979266835273594355.jpg

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Reply 1
Original post by Shas72
iam not able to solve Q 12.
I solved the diff eq and got 1/100[ln(P/100-P)=Kt/100+C15961171999881979266835273594355.jpg

Can you upload your working?
You use the two initial conditions to determine k and c.
Note I guess P is in millions of people?
(edited 3 years ago)
Reply 2
Original post by mqb2766
Can you upload your working?
You use the two initial conditions to determine k and c.
Note I guess P is in millions of people?

So when P= 50 million , t=0 and P= 60million, t=10 years right?
Reply 3
Original post by Shas72
So when P= 50 million , t=0 and P= 60million, t=10 years right?

P=50 when t=0. Otherwise it doesn't make sense. It should state in the question though.
Reply 4
Original post by mqb2766
P=50 when t=0. Otherwise it doesn't make sense. It should state in the question though.

Ok i have also done a silly mistake. Let me work it out and see if I get the right ans. Thanks!!
Reply 5
Original post by mqb2766
P=50 when t=0. Otherwise it doesn't make sense. It should state in the question though.

So c=0 and k=1/10ln3/2 right?
Reply 6
Original post by Shas72
So c=0 and k=1/10ln3/2 right?

I've not worked it through fully, but upload your working if you want it checked.
Reply 7
p

Original post by mqb2766
I've not worked it through fully, but upload your working if you want it checked.

ok sure.
Reply 8
Original post by mqb2766
I've not worked it through fully, but upload your working if you want it checked.

1596119838503514999332639962898.jpg
Reply 9
Looks fine so far
Reply 10
Original post by mqb2766
Looks fine so far

So when P=60, t=10 right?
Original post by Shas72
So when P=60, t=10 right?


As far as I can tell. That will give you k.
Reply 12
Original post by mqb2766
As far as I can tell. That will give you k.

Yeah I know that. So I got k =1/10ln1.5
Original post by Shas72
Yeah I know that. So I got k =1/10ln1.5

Seems ok.
Reply 14
Original post by mqb2766
Seems ok.

I dont get the ans. The textbook ans is 73.4 million correct to 3sf
Original post by Shas72
I dont get the ans. The textbook ans is 73.4 million correct to 3sf

I get that answer using your model.
Original post by Shas72
iam not able to solve Q 12.
I solved the diff eq and got 1/100[ln(P/100-P)=Kt/100+C15961171999881979266835273594355.jpg


Why make things difficult for yourself? Try rotating your book 180 degrees. That should make things easier.
Original post by Plücker
Why make things difficult for yourself? Try rotating your book 180 degrees. That should make things easier.

I'm sure OP is reading their book the right way up. They have just uploaded the image wrong...
Original post by 5hyl33n
I'm sure OP is reading their book the right way up. They have just uploaded the image wrong...

Let me think about that.


You might be right.
Reply 19
Original post by mqb2766
I get that answer using your model.

Ok let me try

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