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I am looking for a function based on remaining time. To start with I can use a function which returns a value between [0,1] based on how much time is remaining to finish.

For eg: The total time for the event is 3 hrs i.e. 10,800,000 ms. At the start of the event the function should return value of 0. At half time i.e around 5,400,000 ms remaining time the function should return value of 0.5 at the end of the time i.e when few milli seconds are left, I should get a value close to 1.

i.e this can be a linear function.

I would appreciate if someone can point me in the right direction to model this simple problem. I am new to mathematical modelling.

Thanks!

Alok
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    So you want a linear function where $f(0) = 0$ and $f(10800000) = 1$. Find the slope of the line. Done. – Sean Roberson May 10 '20 at 04:38
  • Thanks @SeanRoberson . This is what i am planning to do as well. When i started writing the question i was looking for a generic function for different events (trading instruments in this case). I stumbled upon https://math.stackexchange.com/questions/57429/functions-similar-to-log-but-with-results-between-0-and-1 which would be nice. .. but in my case I can simply find the slope of the function for each trading intrument separately. That would be much simpler. – Alok May 10 '20 at 07:39

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