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Math help: exponential function

Discussion in 'Off Topic [BG]' started by Figjam, Sep 10, 2005.


  1. Figjam

    Figjam

    Aug 5, 2003
    Boston, MA
    Given 3 points: A(1,20) B(5,10) C(9,5)
    Create an exponential function thru points A, B, C. Find the equation with y in terms of x. ...the formula that was given to do this is (y= a * b (x+c(/d))
     
  2. Brad Barker

    Brad Barker Supporting Member

    Apr 13, 2001
    berkeley, ca
    should that "*" be a "^"?

    what you do is make three equations, given those data points.

    you have:

    x_1 = 1, y_1 = 20,
    x_2 = 5, y_2 = 10
    x_3= 9, y_3 = 5

    plug those into the general equation.

    now you have a system of three equations--you can now solve for three constants!


    ...trouble is... looks like you have four constants in there. :meh:
     
  3. Figjam

    Figjam

    Aug 5, 2003
    Boston, MA
    Its a multiplication sign.

    whats the underscore?


    The end goal is for one equation to graph it.
     
  4. Brad Barker

    Brad Barker Supporting Member

    Apr 13, 2001
    berkeley, ca

    umm...

    i think you mean

    y = a*b^[(x+c)/d] ...?


    but there's one letter too many. :meh:
     
  5. Figjam

    Figjam

    Aug 5, 2003
    Boston, MA
    Sorry it was typed wrong originally,you did it right.

    Im as confused as you are on the 4th thing though, but one equation is somehow needed in the end.
     
  6. Brad Barker

    Brad Barker Supporting Member

    Apr 13, 2001
    berkeley, ca
    i used the underscore to denote a particular value of x with a corresponding particular value of y.

    replace "1,2,3" with "A,B,C." then it would match up better and make more sense, maybe, since A, B, and C are what the points are called.
     
  7. Brad Barker

    Brad Barker Supporting Member

    Apr 13, 2001
    berkeley, ca

    hmm... i'm going to work on this one. (just finished my own hw. :D )
     
  8. Brad Barker

    Brad Barker Supporting Member

    Apr 13, 2001
    berkeley, ca
    well, i made a graph on excel, and it definitely looks exponential! :p


    it decayed (that is, got smaller as x increased).


    anyway, a trick that you might use is:


    b^(a+c) = b^a * b^c


    --> i think this'll eliminate one of our constants; it just gets folded into our coefficient.

    so my recommendation is to set c=0 in the equation you want to solve for.


    that and a lot of algebra ought to do it. :hyper: