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Wikipedia states that buprenorphine (a.k.a. suboxone) has an elimination half-life ranging from 20 hours to 73 hours, with a mean of 37 hours. Based on a half-life of 37 hours, and assuming 2mg a day for the past month, how many days would it take to be effectively out of one's system?

(Answers to this question should not be considered as a substitute for advice from a medical professional).

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    I'm not so sure this is the right place to get medical advice. But as far as the math is concerned, you need to specify what level of presence is considered "out of your system". Under a half-life assumption, there will always be *some* level of any compound in ones body, it will just eventually reach undetectable levels.2012-01-17
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    I agree with Alex, I'm afraid we really can't answer this question. I would recommend that you consult with a doctor, especially the one who prescribed you the medication (if it is a prescription drug).2012-01-17
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    @Zev *Please* try to avoid using binding closing votes.2012-01-17
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    @Bill: There were already two votes to close. Moreover I consider this question to be something that is clearly inappropriate to answer on this site, and more generally on the internet, and more generally by anyone who is not a medical professional who is familiar with JasonD's specific situation. Perhaps he has a condition that makes the pharmacodynamics of this drug different for him. I don't think closing this question as soon as possible is unreasonable. Finally, Alex's comment above correctly explains that one needs to specify what concentration is considered "not present".2012-01-17
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    I'm really not sure why this question was closed; sounds very much like a word problem in algebra to me, i.e., applied algebra. In any event, there are several half-life calculators available on the web see this one, for instance: http://www.calculator.net/half-life-calculator.html2012-01-17
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    @Zev Since when does *your* opinion represent everyone else? This is a matter or principle, not the specifics of this question.2012-01-17
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    @Bill: I never stated that it did. I consider this to be basically as inappropriate as spam (though certainly with no ill intent on the part of JasonD), and reacted as such.2012-01-17
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    @Zev But it is *not* spam. Please don't use binding close votes for anything but spam. Please let the community decide. I see no need to short-circuit that process here.2012-01-17
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    @3Sphere It is worded as if the asker wants medical advice. Also, a word problem in algebra would come accompanied by the half-life, rather than requiring someone to wikipedia it.2012-01-17
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    I've restated the question to remove any reference to JasonD's personal situation and also added a caveat that takes care of the concern of Alex and me. I've now reopened.2012-01-17
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    @JasonD: Please clarify if this is a question regarding actual, real-life use of the medicine, or if it is simply an algebra word problem to practice differential equations/half-life problems.2012-01-17
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    @Alex I agree that the question should be worded in a neutral fashion, e.g, If a drug has a half-life of X, how much time T is required until the drug has dissipated by Z% ? Ultimately, though, it's just an algebra word problem and I think with these minor adjustments it becomes a reasonable question. I think the OP should have been asked to *improve* the question before closing it and it should only be closed if those improvements are not made2012-01-17
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    @3Sphere, Bill: Given the possible legal ramifications of answers being posted to the question as it was originally asked, I still feel that it was better to err on the side of caution and close first, consider how to improve the question later. In the future will try to avoid using my close vote except when it's the fifth and final one, or when the question is spam.2012-01-17
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    @Zev Thanks for explaining, and for improving the question. It's nicer to newcomers doing that rather than rushing to close questions that need improvement.2012-01-17

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On account of the fact that there is interesting mathematics at play here, I will answer this question. Please do not construe this as medical advice.

Without knowing what level of presence is considered "out of one's system", this question cannot be given a full answer. However, I can give an expression for the amount of substance that will remain after time $t$. All units will be in hours and milligrams. Since the half-life is $37$, the mass of substance $m(t)$ as a function of time satisfies the differential equation $$\frac{d}{dt}m(t)=\frac{\ln 2}{37}m(t)$$ and in addition we have discontinuities introduced each day for the first month by the fact that $m(t)$ increases by $2$ at 24-hour intervals for the first month. At time $0$, the first dose is taken, so $m(0)=2$. Observing that the solution to the differential equation away from the discontinuities is $$m(t_0)e^{-\lambda(t-t_0)}$$ where $\lambda = \frac{\ln 2}{37}$ we get that $m(24) = 2 + 2e^{-24\lambda}$. Repeating in this manner, $$m(48)=2+m(2)e^{-24\lambda} = 2 + (2 + 2e^{-24\lambda}) e^{-24\lambda} = 2+2e^{-24\lambda}+2e^{-48\lambda}$$ and more generally $$m(24n) = 2\sum_{k=0}^n e^{-24k\lambda}$$ for $n\leq 30$, assuming that the month in question has 31 days. After $24\times 30=720$ hours, no more doses will be taken and so we will be away from the discontinuities, thus for $t>720$ we have $$m(t)=m(720)e^{-\lambda(t-720)}=2\left(\sum_{k=0}^{30} e^{-24k\lambda}\right)e^{-\lambda(t-720)}$$ which can be graphed by most mathematics programs, including wolfram alpha (keep in mind that $\lambda$ is a constant with approximate value $.0187$). Once this graph dips below the relevant threshold value, the substance will be "out of one's system".