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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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