Yeah, I agree with you ventilator.

I guess that if neither approach is working there is probably some other problem in the code that needs to be solved.

I did spot a problem in Chaeon's implementation: pow(reductionspersecond,16 / time_step) should be
pow(1-reductionspersecond,time_step/16)

(notice the '1-' and the inversion of time_step/16)