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**mrpace****Member**- Registered: 2012-08-16
- Posts: 63

dT/dt = -k(T-T1)

The question then states that this means that T(t)=T1+Ce^(-kt)

I don't see how they got that...can you help please?

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You will get that if you integrate both sides

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**mrpace****Member**- Registered: 2012-08-16
- Posts: 63

Agnishom wrote:

You will get that if you integrate both sides

maybe you can show me?

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Someone else might do it. I cannot

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,188

hi mrpace

Fisrtly, note that T and t represent different variables here.

One method for solving this is called "separation of variables". You have to get all the T terms on one side and all the t terms on the other

Strictly speaking the dT/dt is not separable like this as it represents 0/0, but it works out ok if you quickly put in integration signs.

Now integrate each side. The right hand side is easy as it is just integrate a constant with respect to t. The left hand side is a natural log.

As D is just the constant of integration you can replace it with ln(C), another constant.

Bring the two log terms together using the rules for logs and then re-write the expression with e to get the required expression.

I've left a few steps for you. Post back if you need more help.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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