using System;

using System.Linq;

​

#nullable enable

​

public class Program

{

    public static void Main()

    {

        TimeSpan start = TimeSpan.Parse("00:05:00.123");

        TimeSpan max = TimeSpan.Parse("00:15:00.23456");

        var repeat = Enumerable.Range(0, 100);

        foreach(var r in repeat){

            var val = Calculate(start, max, r, 0.4);

            Console.WriteLine($"max is: {max} function: {val} has reached max: {val == max}");

        }

    }

    public static TimeSpan Calculate(TimeSpan initial, TimeSpan max, int offsetFactor, double growthConstant)

    {

        if (max < initial)

        {

            throw new ArgumentOutOfRangeException(nameof(max), $"Cannot be lower than {nameof(initial)}.");

        }

​

        double initialValue = (max.TotalMilliseconds / initial.TotalMilliseconds) - 1;

        return TimeSpan.FromMilliseconds(max.TotalMilliseconds / (1 + initialValue * Math.Pow(Math.E, -growthConstant * offsetFactor)));

    }

}