Function that maps low values to [0,1] I'm currently working on a predator prey simulation and have to parameters that are codependent, the attack rate and the survival rate.
The attack rate is mutated within the simulation and determines the survival rate in the following way:

A high attack rate implies a more risky way of hunting, which concludes to a lower survival rate.

The attack rate can be withing 0 and 1, but mostly assumes only low values <0.06. The survival rate is also within 0 and 1 and can use the whole range.
Ultimately, I'm searching a function that maps the attack rate to a sensible survival rate. My current function is very made up: (1-log2(attack rate + 1))**10)


After some more research I found a good solution using eulers function:
exp(-x*attack rate)
In my case the x must be relatively high (x=10)
