Results 1 to 11 of 11

Math Help - Solving an equation.

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    4

    Solving an equation.

    I'm working on implementing an old method for determination of cerebral blood flow in rats. I'm stuck in this equation! It is some years since I've worked with such formulas, and I can not get it to go up.

    I really hope that there is one who will try .. X supposed to be equal to 0.058 / sec


    (A/B)=C* ((exp[X-T*0,32])-1)/X

    A=0,0026 nCi (Curie, measurement of radio-activity)
    B=0,00152 mL/second (Millilitre/sec)
    C=0,074 uCi/mL
    T=20 seconds



    This is the actual equation(11) from the article with values and constants ..:

    Here, x is called k..






    Thanks/ Jakob
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by jakobbokaj View Post
    I'm working on implementing an old method for determination of cerebral blood flow in rats. I'm stuck in this equation! It is some years since I've worked with such formulas, and I can not get it to go up.

    I really hope that there is one who will try .. X supposed to be equal to 0.058 / sec


    (A/B)=C* ((exp[X-T*0,32])-1)/X

    A=0,0026 nCi (Curie, measurement of radio-activity)
    B=0,00152 mL/second (Millilitre/sec)
    C=0,074 uCi/mL
    T=20 seconds



    This is the actual equation(11) from the article with values and constants ..:

    Here, x is called k..






    Thanks/ Jakob
    You cannot solve for X algebraically. A numerical procedure has to be used to get a decimal approximation. Use a graphics or CAS calculator or computer software to solve it.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2010
    Posts
    4
    I've used my 'TexasInstruments TI83' as you describe - and my problem is more accurately that I can not get the same value for X (or k) as the author. I've tried hard and suspect an error in the article.

    Is there anyone who can get the right value of X?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by jakobbokaj View Post
    I've used my 'TexasInstruments TI83' as you describe - and my problem is more accurately that I can not get the same value for X (or k) as the author. I've tried hard and suspect an error in the article.

    Is there anyone who can get the right value of X?
    solve 0.0026/0.00152 = 0.074(Exp[x - 2(0.32)] - 1)/x - Wolfram|Alpha
    Follow Math Help Forum on Facebook and Google+

  5. #5
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    I'm seeing some mixed units in there. A and C, for example, have different units. Have you taken that into account?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Ackbeet View Post
    I'm seeing some mixed units in there. A and C, for example, have different units. Have you taken that into account?
    Good call.

    The OP can edit the input at the Wolfram Alpha link I posted.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    There's something else very strange with that equation. The expression

    e^{k-Tkt'}

    is highly problematic. It appears that the units of T are time, as well as t'. The units of k are inverse time. But the argument of an exponential function is not allowed to have units of any sort: it must be dimensionless. Otherwise, in the Taylor series expansion, you'd have widely varying powers of units being added together.

    Might there be an error in the formula?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Maybe the correct argument is kT-kt'=k(T-t')? That would work in terms of units.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Nov 2010
    Posts
    4
    Great point. I really appreciate your responses. Here you can see how they reach equation (11) .. They want to bring k and t' together lige that because the value of kt' is known.

    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Nov 2010
    Posts
    4
    Quote Originally Posted by Ackbeet View Post
    Maybe the correct argument is kT-kt'=k(T-t')? That would work in terms of units.
    YES - that way I get the right solution. I am very happy and relieved.

    http://www.wolframalpha.com/input/?i...%5D+-+1%29%2Fx

    - Have a good time -
    Last edited by jakobbokaj; November 6th 2010 at 03:53 PM.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Good. My guess about the argument is correct. If you compute the integral and simplify, you get exactly equation 11, but with my argument for the exponential function. Therefore, I conclude that equation 11 contains a typo. Obviously, the authors simply mis-typed it, since they got the correct number for k. That is, they used my argument, not the one they typed up, when they did their computations.

    Cheers.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help solving this equation..?
    Posted in the Algebra Forum
    Replies: 4
    Last Post: April 2nd 2010, 06:20 PM
  2. solving an equation
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 14th 2008, 11:50 PM
  3. solving diff equation w/ bournoulli's equation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 14th 2008, 06:06 PM
  4. solving equation
    Posted in the Algebra Forum
    Replies: 6
    Last Post: August 2nd 2007, 03:15 AM
  5. Help on solving equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: July 26th 2007, 04:01 PM

Search Tags


/mathhelpforum @mathhelpforum