"Exponential decay curve" and "irrational numbers" are two different concepts. (1/2)^N is an exponential decay curve -- which defines the half-life of a radioactive substance. For no integer value of N is the result "irrational".
You are insisting on integer values of N. Which is silly. There's nothing special about integer amounts of time. (1/2)^t is irrational for almost all values of t. Furthermore if you were to write down the half life of any radioactive substance in almost any units of time, you would get irrational numbers for their half life.
I google for things on Bing.
I bang things on google.
If you think the system is working, ask someone who's waiting for a prompt.