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Forming differential equations

Hi, I've been given a question that I feel I can complete but I first need to form the equation y(t) which I'm not 100% sure how to do. I've attatched a photo of the first part of the question.

Would y(t)=32,000,000*t*x where x is the exchange rate?

Thanks
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Original post by Substitution
Hi, I've been given a question that I feel I can complete but I first need to form the equation y(t) which I'm not 100% sure how to do. I've attatched a photo of the first part of the question.

Would y(t)=32,000,000*t*x where x is the exchange rate?

Thanks


y(t) = 32000000tx isn't a differential equation. It's just a function of t.

You know that the banks process a certain amount of money each day and it all becomes euros. How much of the money that they process will be in pounds?
Original post by morgan8002
y(t) = 32000000tx isn't a differential equation. It's just a function of t.

You know that the banks process a certain amount of money each day and it all becomes euros. How much of the money that they process will be in pounds?


Initially it would be 32 million right? because nobody will have euros but then it'll change to be p=32000000-xq with p=pounds, x=exchange rate and q= euros?
Original post by Substitution
Initially it would be 32 million right? because nobody will have euros but then it'll change to be p=32000000-xq with p=pounds, x=exchange rate and q= euros?


If p is the number of pounds exchanged per day and q is defined similarly for euros, yes.


Also, what can you say about the ratio of pounds to euros taken in by the banks compared with the national ratio?
Original post by morgan8002
If p is the number of pounds exchanged per day and q is defined similarly for euros, yes.


Also, what can you say about the ratio of pounds to euros taken in by the banks compared with the national ratio?


That's what I meant :tongue:.

Not sure how to define that one, because the national ratio would be hard to define in terms of p and q because it would be the amount of euros that come into circulation from a bank would change every day? I'm probably making this more complicated than it needs to be,

Thanks for your help
Original post by Substitution
That's what I meant :tongue:.

Not sure how to define that one, because the national ratio would be hard to define in terms of p and q because it would be the amount of euros that come into circulation from a bank would change every day? I'm probably making this more complicated than it needs to be,

Thanks for your help


We know that the value of euros nationally is y(t) and the total national currency is £64 billion. So we can just divide to find that ratio.
Also, the ratio of money that comes into the banks is equal to the national ratio. Remember p and q aren't constant, they change as more euros enter country.
Original post by morgan8002
We know that the value of euros nationally is y(t) and the total national currency is £64 billion. So we can just divide to find that ratio.
Also, the ratio of money that comes into the banks is equal to the national ratio. Remember p and q aren't constant, they change as more euros enter country.


Okay that makes sense..

So dq/dp=y(t)/32000000-xq correct?

Still not sure where to go.. sorry!

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