Math Is Fun Forum

lisa123

Member

Registered: 2007-11-11

Posts: 5

drug levels

If 2.5 mg of a drug with half-life of 14 hrs is taken every 24 hrs, then to what level does the drug build up over time?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: drug levels

24 hours is 24÷14 ≈ 1.714 half-lives.

Therefore, if someone has x mg of drug in their system, then 24 hours later they will have x*0.5^1.714 in them.

We want to find the value of x that makes the amount go down by 2.5 mg in 24 hours. (That way, the amount that goes will be countered by taking the new amount each day)

So we have x - x*0.5^1.714 = 2.5.

x(1 - 0.5^1.714) = 2.5

x = 2.5/(1 - 0.5^1.714) ≈ 3.60 mg.

So over time, the person will eventually have around 3.6 mg of the drug in them.

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