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# Help please - modelling with differential equation AQA C4 watch

1. Hi everyone,

I am stuck on another question in my AQA book.

It is on modelling with differential equations.

11F 3) Mould is spreading through a piece of cheese of mass 1kg in such a way that at a time t days, x kg of the cheese has become mouldy where: -

dx/dt = 2x(1-x)

Given that initially 0.01 kg of the cheese is mouldy.

a) Show that x = [e^(2t)] / [99+e^(2t)]

b) Calculate after how long 0.99 kg of the cheese will be mouldy, giving your answer to the nearest hour.

I've got a few more questions but I won't post them because hopefully, if this one is explained, I'll be able to answer the rest myself.

Ross
2. What you need to do is divide through by 2x(1-x) and then integrate both sides w.r.t. t. i.e. you'll get:

remember your constant of integration, and have a look at what it says in the question for the initial weight (i.e. the weight when t=0).

For part b), you have a formula for x in terms of t, you're given a value for x, so just re-arrange for t (remembering to multiply by 24 because the formula gives time in days, not hours).

As for the integration, just think partial fractions.
3. Thanks for helping out. I'll have another go at it and hopefully I'll be able to do it now.

Will post back to confirm success !
4. If you need something to check against, I tried it and got 110 hours
5. (Original post by rosschambers1987)
Hi everyone,

I am stuck on another question in my AQA book.

It is on modelling with differential equations.

11F 3) Mould is spreading through a piece of cheese of mass 1kg in such a way that at a time t days, x kg of the cheese has become mouldy where: -

dx/dt = 2x(1-x)

Given that initially 0.01 kg of the cheese is mouldy.

a) Show that x = [e^(2t)] / [99+e^(2t)]

b) Calculate after how long 0.99 kg of the cheese will be mouldy, giving your answer to the nearest hour.

I've got a few more questions but I won't post them because hopefully, if this one is explained, I'll be able to answer the rest myself.

Ross
Did you ever solve that question? I'm stuck on finding the constant of integration. I get 1/2 (lnx + ln(1-x)) = t+c but can't find c so can't move on. Any help would be gratefully accepted.
6. (Original post by maggiehodgson)
I get 1/2 (lnx + ln(1-x)) = t+c but can't find c so can't move on. Any help would be gratefully accepted.
You need to input the initial conditions to find c. Check back to the question.
7. (Original post by maggiehodgson)
Did you ever solve that question? I'm stuck on finding the constant of integration. I get 1/2 (lnx + ln(1-x)) = t+c but can't find c so can't move on. Any help would be gratefully accepted.

I have just wasted time working through a question that is over a year old.

8. Thanks for your advice. I would if I knew how but you might not have noticed that my status is "new member" and as such I'm am unfamiliar with how to use TSR.

Sorry you wasted an hour of your time. On my behalf you need not waste any more. The problem is solved.

With your reaction to me I do feel that I won't be using TSR again. I have been made to feel quite uncomfortable or if I do I hope I am tolerated a little more.

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