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Rewriting a base; Formula of a Reciprocal Function

  1. Sep 8, 2011 #1
    1. The problem statement, all variables and given/known data

    I have a function, y = 6*e^0.4x. How would I convert the regular form, y=a*e^bt to the form y= at^b?

    2. Relevant equations

    y = 6*e^0.4x

    3. The attempt at a solution

    I've tried to take the log of both sides, but if I do that, then "y" becomes a log, and I can't remove that "log*y" unless I put the "base" of the formula back down.




    And another quick problem:

    1. The problem statement, all variables and given/known data

    I have a set of data, t and C (hours and concentration; g/L, respectively). Somehow, by using that data, I can solve for the concentration equation, 1/(a+bt).

    2. Relevant equations

    Given data:
    t (h) 1.0 2.0 3.0 4.0 5.0
    C (g/L) 1.43 1.02 0.73 0.53 0.38

    Concentration equation, 1/(a+bt).

    3. The attempt at a solution

    Not a clue;I'm supposed to find the coefficients of the concentration equation by graphing the data that was received. I've tried to graph a graph of C vs. T, and tried to take the reciprocal of that equation, but it didn't work. I'm supposed to plot the above data in such a way, that the coefficients of the concentration formula can be solved. Any ideas on how I should go about finding the a/b values for the formula?


    Thanks in advance for your assistance.
     
  2. jcsd
  3. Sep 8, 2011 #2

    wukunlin

    User Avatar
    Gold Member

    for your first question:

    let's say
    [tex]A = e^a[/tex]
    then
    [tex]e^{ab} = (e^a)^b = A^b[/tex]

    does that help?
     
  4. Sep 8, 2011 #3
    Thanks Wukunlin, but I know I can combine e with its exponent.
    Let me just replace that "x" with "t".
    Ie: y = 6e^0.4t can be written as y = 6(1.4918...)^t - I need to find a way to get the "t" next to the base, and somehow get the base as the exponent - in the form y = at^b. I'm just confused about how I should go about doing this.
     
  5. Sep 8, 2011 #4

    wukunlin

    User Avatar
    Gold Member

    as far as I know that is impossible. What that does is turning an exponential function into a power function.
     
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