I am not exactly sure if there is a true formula for half life or the application of an integrated formula is required depending on the number of half life the original substances had to undergo?

Perhaps you are looking for an equation like this:

y = 1/(2^t)

Where y = how much is left of original material, t = number of half lives

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In terms of chemistry

FOR ZERO ORDER REACTIONS

[A] = [A0] - kt

t 1/2 = [A0]/2k

Where:

t 1/2 = half life

[A] = current concentration

[A0] = initial concentration

k = reaction constant

t = time

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