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Math Help - Convertion/translation of two equations

  1. #1
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    Norge
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    Talking Convertion/translation of two equations

    I have two tasks that I'm unable to work out, and I hope someone could help me :)


    TASK 1:
    There are three unknown exponential functions:
    y1 = f1 (t);
    y2 = f2 (t);
    y3 = f3 (t):


    By measuring the values of t and yi, you get a linear relation between:


    Yi = logci (yi) (log to the base of ci)
    and t:
    Yi = logsi (yi) = Ait + Bi (log to the base of si)




    Describe the function f1 in the following way:
    y1 = f1 (t) = Ce^(lambda*t)


    The values are
    i 1 2 3
    Ai -1.25 1.53 -1.95
    Bi 1.19 1.1 1.95
    si 3.76 0.32 0.3


    (i is always the base of A, B, s, Y and y)




    TASK 2
    Translate the equation
    ln (y) = a ln (x) + b


    to


    y = f (x) = cx^r


    when a=1.5486 b=0.9309
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  2. #2
    Super Member
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    Re: Convertion/translation of two equations

    I'm a little confused about si and ci in Task 1. If \log{y} = Ax + B, then you take e to both sides to get y=e^{Ax+B}=Ce^{Ax} where C=e^B.

    It looks like Task 2 is a similar idea with \log{x} instead of x:
    \log{y} = A \log{x} + B
    e^{\log{y}} = e^{A \log{x} + B}
    y = e^{A \log{x}}e^B, and setting C=e^B as before,
    y = Cx^A
    The identity x^A=e^{A \log{x}} follows from the power rule for logarithms.

    - Hollywood
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  3. #3
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    Sep 2012
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    Norge
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    Re: Convertion/translation of two equations

    Thanks for the assistance! I managed to work it out by plotting in the values and using some of what you wrote

    Cheers!
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