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Math Help - Explicit mathematical expression

  1. #1
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    Explicit mathematical expression

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

    As an explicit mathematical expression of T(t)?
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    Quote Originally Posted by sazzy3 View Post
    How would you write the function: dT/dt= -k(T-A)

    As an explicit mathematical expression of T(t)?
    solve the differential equation, note that it is separable, so we have

    \frac {dT}{T - A} = -k~dt

    now integrate both sides and then solve for T (don't forget your arbitrary constant)
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    question 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?
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    Quote Originally Posted by sazzy3 View Post
    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?
    we are not using a definite integral here, it is indefinite. and \int -k~dt = -kt + C
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    continued

    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?
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  6. #6
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    Quote Originally Posted by sazzy3 View Post
    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?
    if you have T - A on the left, to solve for T you would ADD A to both sides... and make sure -kt + C is the power of e, not just the -kt, which is what you typed
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  7. #7
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    continued

    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.
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  8. #8
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    Quote Originally Posted by sazzy3 View Post
    Was this part even correct? or had i gone wrong before this point?

    [T-A]=e^(-kt +C)
    you are ok up to this point.

    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.
    as i said, you have -A on the left side of the equation, you must ADD A to both sides to solve for T
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