There is no "whole time". When you take a medicine, a certain portion of it gets into your blood stream and permeates your body. Immediately your liver and other body parts start deactivating and removing it. If the half life is 12 hours, then at 12 hours half of it is gone, so you are down to 50% of the peak level. In another 12 hours, you are down to 25%, then 12.5%, and after about 5 half lives, so little is left we consider it pretty much gone, but trace amounts actually remain in your body for longer.

It's also useful to know that if you keep taking the drug, let's say for a condition like epilepsy where you need a constant minimum amount of drug in the body, at first it starts to accumulate in your body as you are adding more drug before the previous dose is cleared, and it takes about 5 half lives before you reach a steady state or plateau, where the blood level is the same every day. It still shoots up to a peak after each dose, and then drops somewhat before the next dose, but the peaks and valleys are the same every day at steady state, so you can be confident that even at the lower blood level just before each dose, there's enough drug to prevent seizures.

Half life is also useful to know if you stop a drug, because you know that in about 5 half lives it'll be pretty much gone.

Sometimes half life can change due to some other drug or medical condition, and that is useful to know as it may mean you have to adjust the dose of your drug to correct for that. In overdoses, sometimes the mechanisms that clear drugs from the body can't scale up to deal with high drug levels, and the half life is longer and it takes longer than expected to recover.

I may suspect you have not gotten told what half-time is? :-)

Halftime is when half of the product is gone. Let's say you have 100mg after 10 minutes is only 50mg still active, again after 10 minutes is 25mg still active, 10 min more 12.5 then +10 minutes 6.25mg, now 10 min later 3.12mg and that keeps going on.

For every 10 minutes is the product's strength half. It's whole time depends on when, what is left, is too little to do anything.

So the idea of half-life is a bit simplified for biological processes. The way half-life is taught in school is usually with radioactive decay. Radioactive decay follows a first order rate of reaction. What this means is the rate of reaction is directly proportionally to the amount of substance. If you have half as much, it decays half as slowly.

Many other reactions have more complicated kinetic orders. There are second order reactions where reactions go four times faster if you double the reagent. Zero order reactions where the rate is not affected by the amount of something. You can have fractional order reactions that speed up as the concentration of a reagent decreases. A reaction can also have different orders for each reagent or even be catalyzed by some small amount of something to speed it up. Also, there can be a limited amount of certain reagents in the body meaning the order of the reaction can change as something is broken down.

So, for instance say you have a drug that is a zero order reagent. It is broken down at a rate of 1 g/hrs. You take two grams. Half life is 1 hour. After that hour, half life will be 30 minutes. 30 minutes from that, 15 minutes. You get the idea.

Finally to answer your question, the half-lives are written at expected does. It can not necessarily be extrapolated to tell when it will all be out of the body, but it is a useful tool for healthcare providers.

We use half life because, quote simply, that's how the laws of thermodynamics work in chemistry. I know that's kind of an unsatisfying answer, but answering why it works that way is kind of like asking why radioactive elements decay in a half-life fashion.

When reactions generate a half life, it becomes very difficult to say precisely when the reaction will stop proceeding entirely. Additionally, even if you knew precisely how long it would take, a large percentage of that time would be taken by the tail end of the reaction, where blood levels of the drug are so low they are ineffective.

In short, we use half life because it gives the amount of time that the concentration of the drug is in your system is at the level we need it to be for it to be beneficial and do its thing.

Basically, what you really care about is "How likely is it that any given molecule of this stuff will randomly break down at any time?" because if you know that and you are working with billions and billions of molecules, that gives you a very good idea how long the drug will last overall.

But even drugs with short shelf-lives are stable enough to make that probably very low, so instead of saying "In any given second there is a 0.000000000000000000000000000000001 percent chance of one molecule breaking down." we measure it indirectly instead. And that's what a half-life is: it takes the probability of each molecule breaking down and is an estimate of how long it will take for there to only be half of the substance left.

Let's use a model as an example: let's say you have a school of 1000 children, and you give them each a ten-sided die. You have them all roll the die at the same time, and every child who rolls a 10 gets eliminated.

In the first round, about 100 students will be eliminated, leaving 900. Next about 90 are eliminated, leaving 810. This keeps going with the number eliminated getting lower or lower until eventually there are only one or two students left and it becomes very hard to predict how long it will take to eliminate the last few people. The number or rounds necessary to get to about 500 students would be the half-life in this scenario.

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Generalizing A LOT, because we need to know how often we administer the medication in order to have a stable concentration. We need to do that not when it is completely cleared but when it is still active.