a non linear curve that returns values between 0 and 1 but the x axis range is very long.

212 Views Asked by At

I am new to mathematical modelling and trying to understand how I can fit a non linear curve for my requirement below

  • The curve should increase from 0 and finish at 1 within the given range of x. X axis is time and it starts at 9 am and finishes at 4 pm. (can be different start time and end time for other events).
  • at the start of the time i.e. 9 am i should get a value of 0. At the end of the curve i.e. 4 pm, I should get a value of 1.
  • as the time progresses, initially the growth is slower and as the end time approaches, the the growth rate should increase. (function of remaining time).

for eg: curve can range between [0,0] to [10000,1] or [0,0] to [1000000,1]

I found many functions that return value between 0 and 1 for a very small range of x. I am not sure how to do this for a large range of x.

I look at time in total milliseconds, but I can also check the time in hours that will reduce the X range a lot.

Thanks.