How would you write the function: dT/dt= -k(T-A)

As an explicit mathematical expression of T(t)?

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- Mar 24th 2009, 12:04 AMsazzy3Explicit mathematical expression
How would you write the function: dT/dt= -k(T-A)

As an explicit mathematical expression of T(t)? - Mar 24th 2009, 12:39 AMJhevon
- Mar 24th 2009, 12:50 AMsazzy3question continued
So now i have

dT/T-A=-k dt

i get integral from T to T0 1/T-A dT= integral from t to t0 -k dt

then

ln [T-A] integral from T to T0= integral from t to t0 -k dt

then

ln [T-A]= -kt

then

[T-A]= e^-kt

Is this correct? - Mar 24th 2009, 12:56 AMJhevon
- Mar 24th 2009, 01:00 AMsazzy3continued
So i just needed to change it to:

ln [T-A]=-kt +c

then

[T-A]=e^-kt +c

then for just an expression of T(t)

do i go

T= Ae^-kt +c

If not can you please show me where i have gone wrong and how it should be done? - Mar 24th 2009, 01:03 AMJhevon
- Mar 24th 2009, 01:10 AMsazzy3continued
Was this part even correct? or had i gone wrong before this point?

[T-A]=e^(-kt +C)

and i had to find an explicit mathematical expression of T(t)

so have i done that by then making the equation

T=A e^(-kt +C)??

Very confused. - Mar 25th 2009, 08:31 AMJhevon
you are ok up to this point.

Quote:

and i had to find an explicit mathematical expression of T(t)

so have i done that by then making the equation

T=A e^(-kt +C)??

Very confused.

**-**A on the left side of the equation, you mustA to both sides to solve for T**ADD**