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#1 2013-10-26 18:31:55
- mrpace
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- Registered: 2012-08-16
- Posts: 88
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
Re: Quick calculus question
You will get that if you integrate both sides
'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'
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#3 2013-10-26 18:54:31
- mrpace
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- Registered: 2012-08-16
- Posts: 88
Re: Quick calculus question
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
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'
I'm not crazy, my mother had me tested.
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#5 2013-10-26 20:56:44
- Bob
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- Registered: 2010-06-20
- Posts: 10,643
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. 
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
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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