# How do I calculate a "full-life" from a half-life of substance elimination? [closed]

The half-time of carbon monoxide disappearance from blood under normal recovery conditions while breathing air showed considerable between-individual variance. For carboxyhaemoglobin concentrations of 2–10%, the half-time ranged from 3 to 5 h (Landaw, 1973); others reported the range to be 2–6.5 h for slightly higher initial concentrations of carboxyhaemoglobin (Peterson & Stewart, 1970).

(from here)

To get a "full-life" (or the best approximation of it), should I multiple it by 2 or 6.64 (99%)? Is carboxyhaemoglobin's "full-life" in bloodstream 4-13 or 13-86 hours? That's a huge difference

There is no such thing as a "full-life", because in most relevant mathematical models (the simplest and most common being first-order exponential decay), the time required for all the the substance to be gone is infinite.

For example, the half-life is marked on the following graph as $$t_{1/2}$$. Is two times the half life a "full-life"? What must $$t$$ be for the quantity (concentration, number of particles, whatever) to become zero? Based on my first paragraph you should be able to answer these questions.

What you can do, given data or an equation, is calculate the amount of time required for the quantity to drop to a specified amount. For instance, you could decide that you'd like to know the time it takes for the CO concentration to drop by 90% or 99% or 99.9% from the initial level. A rule of thumb (which can be derived from the exponential decay equation) is that the quantity will be depleted by around 99% in approximately seven half-lives. You could derive a similar relations for any desired percent. Which percent to choose for the cutoff of interest is at the discretion of the person doing the analysis, and different fields and contexts have different standards. The substance will never be "completely" gone, but there may be a meaningful threshold beyond which it becomes negligible.