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Math Help - Exponential modeling problem

  1. #1
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    Exponential modeling problem

    Hi, I"m having trouble working out this problem.
    Using data provided, develop a model in the form y = y_0e^{kt} to state the relationship between mass, m, and the length, l, of the fish.

    Here is the data:
    l 10.1 25.0 32.6 35.4 43.8 45.5 55.7
    m 51 236 520 660 1250 1425 2590

    I tried doing this with simultaneous equations, using two sets of data points, but that just didn't work. Does anyone know how one would do this?

    David.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Bucephalus View Post
    Hi, I"m having trouble working out this problem.
    Using data provided, develop a model in the form y = y_0e^{kt} to state the relationship between mass, m, and the length, l, of the fish.

    Here is the data:
    l 10.1 25.0 32.6 35.4 43.8 45.5 55.7
    m 51 236 520 660 1250 1425 2590

    I tried doing this with simultaneous equations, using two sets of data points, but that just didn't work. Does anyone know how one would do this?

    David.
    You want a realtionship of the form m=m_0e^{kl}. Take logs then you have:

    \log_e(m)=k \times l + \log_e(m_0)

    so now use linear regression using \log_e(m) rather than $$m

    CB
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  3. #3
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    OK I have the linear regression

    So I have found that the y intercept of the graph is my ln(m_0) and that the gradient will give me my k.
    But I have the y axis as unit increments, 1, 2, 3 and the x axis as 5 unit increments, 5, 10, 15, etc
    If I take to vertical lines say from 15 and 20 up to my regression line and then draw across to get their corresponding y-axis values, can I use the gradient formula to get the correct gradient. what I"m asking is the fact that I have used different increments for the y and x axis going to affect me using the gradient formula.

    David.
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  4. #4
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    Ok, I think that was a silly question. But probably not in the context of using graph paper and working out the gradient graphically, but if I use the gradient forumula I have found that it doesn't matter what the increments are.
    thanks.
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