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MathGroup Archive 2005

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Re: help on kind of 'inverse exponential' function ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg61900] Re: help on kind of 'inverse exponential' function ?
  • From: dh <dh at metrohm.ch>
  • Date: Fri, 4 Nov 2005 05:11:21 -0500 (EST)
  • References: <dkco12$q9g$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hello Søren,
I assume by faster decay you mean "faster towards minus Infinity".
As Exp[t] approaches + Infinity with increasing speed, -Exp[t] will 
approach -Infinity with increasing speed.
Now, do you have some futher conditions? E.g. is the value for t=0 
given. Asssume we want f[0]=1, then we need to add a constant:
2-Exp[t]
You will note that our function hits zero with a bang. The slope is not 
zero! If this is not o.k. you will have to use an S-shaped curve. But 
let's assume it's o.k.
Further if you want to control the decay rate you could use:
2-Exp[lam t]
where increasing lam increases the rate.
You could also request that at t0, f[t0]=0 by:
2-Exp[Log[2] t/t0]
or you may even specify t0 and control the rate by:
a + (1 - a)Exp[Log[a/(a - 1)]t/t0
where a now controls the rate and should be larger than 1.
e.t.c.
Daniel


Søren Merser wrote:
> hi
> 
> is there a way to express kind of exponential decay,  in such a way that 
> decay is slow in the beginning getting faster as time goes by?
> 
> regards soren 
> 


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