The half-life of a drug is the time taken for the plasma concentration of a drug to reduce to half its original value. Half life is used to estimate how long it takes for a drug to be removed from your body.
For example: The half-life of Ambien is about 2 hours.
So if you take ambien after 2 hours the plasma concentration will be reduced to half, after 2 more hours the remaining blood levels will be reduced by another half - so a quarter will be left. Two hours later another half will be removed leaving one eighth and so on. Generally it is considered that it takes 5.5 half-lives for a drug to be removed from the body, in that it is considered to no longer have a clinical effect.
So for Ambien it would take approximately 11 hours (2 hours X 5.5) to be eliminated from your body.
Elimination of a drug varies from person to person due to factors like age, weight, other medications taken, or other medical conditions present, also kidney function, liver function etc. Therefore half life is used as a guide or an estimate of how long it may take for the drug to be removed from the body.
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