How to smooth a projected value obtained with a multiplicator in a time series?

Question

I have a time series chart where each bar interval = 600 seconds. Each bar accumulates a number of transactions in a variable called 'volume'.

The goal is, while the current 10 mn bar is forming in real time, to anticipate the final volume value it will accumulate. So I do a projection with a 'Multiplicator' that will multiply current intrabar volume in relation to remaining time in the bar. So if 1mn has elapsed, I will project volume as x10, because 600/60 = 10.

Here is the calculation:

    SecondsPerBar = 600; // 10 mn
    TimeElapsed = 60; // 1mn... just an example, this is reevaluated each second.
    Multiplicator = SecondsPerBar / TimeElapsed;
    Projection = volume * Multiplicator;

This works fine, the problem is that in the beginning of the bar, the projection is usually much too strong, but it gets more accurate as the bar develops.

Is there a way to smooth the projection with inverse exponentiality, so at the beginning of the bar the projection will be less strong thus more smoothed, and the smoothness will loose intensity as the bar develops, and be nil at end of bar? What's the proper way to achieve this?