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Math Help - Reducing exponential laws to linear form????

  1. #1
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    Reducing exponential laws to linear form????

    Hi folks!
    I was wondering if any kind people out there could work throught the following question and explain for me as i must admit i am lost!!

    atmosperic pressure p is measured at varying altitudes h and the results are shown below:

    Altitude h m pressure p cm
    500 73.39
    1500 68.42
    3000 61.60
    5000 53.56
    8000 43.41

    show that the quantities are related by the law p = a e(to the power of little k and little h) kh
    where a and k are constants. Determine the values of a and k and state the law. also find the atmospheric pressure at 10,000m

    if you can help i will bow down to thee! :-)

    Thanks




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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by adonis1234 View Post
    Hi folks!
    I was wondering if any kind people out there could work throught the following question and explain for me as i must admit i am lost!!

    atmosperic pressure p is measured at varying altitudes h and the results are shown below:

    Altitude h m pressure p cm
    500 73.39
    1500 68.42
    3000 61.60
    5000 53.56
    8000 43.41

    show that the quantities are related by the law p = a e(to the power of little k and little h) kh
    where a and k are constants. Determine the values of a and k and state the law. also find the atmospheric pressure at 10,000m

    if you can help i will bow down to thee! :-)

    Thanks




    P = Ae^{kh}

    Take logs of both side:

    ln(P) = ln(Ae^{kh}) = ln(A) + ln(e^{kh}) = kh + ln(A)

    Note how similar this is to the equation of a straight line (y = mx +c) ?

    Plotting ln(P) against h gives a gradient of k and y-intercept of ln(A).
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