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MathGroup Archive 2001

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Re: making a function of two coordinates

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31635] Re: [mg31617] making a function of two coordinates
  • From: BobHanlon at aol.com
  • Date: Mon, 19 Nov 2001 03:11:17 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 2001/11/18 7:20:44 AM, veezdREMOVETHIS at hotmail.com writes:

>I have got two coordinates out of graph. The line through the
>coordinates could be described as:
>
>y = U * e^(a * t)
>
>(e is Exponetial e (approx. 2.37))
>
>t is the x-value, I have give two points (t1,y1) and (t2,y2)
>
>I have tried several things (Solve and Fit for example), but I can't
>get the function.
>Does anyone know what should be the input to let Mathematica solve the
>a and U in the formula.
>

Clear[a,t,y,U];

y[t_] := U*Exp[a*t];

Log[y[t]] // PowerExpand

a*t + Log[U]

Solve[{Log[y1] == a*t1+Log[U], Log[y2] == a*t2 +Log[U]}, {a, 
      U}]//Flatten

{a -> (Log[y2] - Log[y1])/
    (t2 - t1), 
  U -> E^((t1*Log[y2] - t2*Log[y1])/
     (t1 - t2))}

{y1, y2} == Simplify[{y[t1], y[t2]} /. %]

True


Bob Hanlon
Chantilly, VA  USA


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