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 >