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#1 2013-10-26 18:31:55

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

Quick calculus question

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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#2 2013-10-26 18:48:32

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,940
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Re: Quick calculus question

You will get that if you integrate both sides


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#3 2013-10-26 18:54:31

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

Re: Quick calculus question

Agnishom wrote:

You will get that if you integrate both sides

maybe you can show me?

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#4 2013-10-26 19:16:52

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,940
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Re: Quick calculus question

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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#5 2013-10-26 20:56:44

bob bundy
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Registered: 2010-06-20
Posts: 7,182

Re: Quick calculus question

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.  smile

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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