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Exponential Decay with Matrices

  1. Mar 6, 2012 #1
    1. The problem statement, all variables and given/known data
    6. Three disease-carrying organisms decay exponentially in seawater according to the following model: P(t) = Ae-1.5t + Be-0.3t + Ce-0.05t

    t 0.5, 1, 2, 3 , 4, 5, 6, 7, 9
    p(t) 6, 4.4, 3.2, 2.7, 2, 1.9, 1.7, 1.4, 1.1

    Estimate the initial concentration of each organism (A,B,C) given the measurements above


    2. Relevant equations
    P(t) = Ae-1.5t + Be-0.3t + Ce-0.05t


    3. The attempt at a solution
    I was thinking of using some kind of matrices but i am having trouble setting the problem up.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 6, 2012 #2

    gneill

    User Avatar

    Staff: Mentor

    Looks like a curve fitting problem where you want to do a fit to an arbitrary function with unknown coefficients.

    If you just need a crude estimate, pick three samples, plug the time values into the equation and reduce the exponential terms to "constants" multiplying A, B, and C. You'll have three equations in three unknowns. If you're ambitious, do the same for several sets of samples, average the results.

    If you have access to any math packages you can probably find subroutines that will fit your function to the data... For example, MathCad has the genfit() function that would do it.
     
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