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Particular Solution

  1. Apr 6, 2004 #1
    Here is the problem...

    Find the exponential function [tex]y=Ce^{kt}[/tex] that passes through the points (0,4) and (5,1/2).

    Just by looking at the problem, I know...

    [tex]y=4e^{\frac{-3x \ln{2}}{5}}[/tex]

    ...works, but how do you actually work out the problem? I've done it before given a point and the slope at that particular point, but I don't really know how to do this.
     
  2. jcsd
  3. Apr 6, 2004 #2
    y=Ce^(kt)

    4=Ce^(k*0)
    C=4

    .5=4e^(k*5)
    (1/8)=e^(5k)
    ln(1/8)=5k
    ln(1/8)/5 = k

    Now that you have k and C, the problem's done!
     
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