Help: estimated amount of drug in the body with a daily dosage

Hello, I have this problem that I can't solve. I am looking for a way, how to plot estimated amount of a drug on a time axis. It's easy to do with the intial first dosage, but I don't know how to account for more dosages.

So, we know: D: Daily drug dosage (example: 25mg) H: Half-life of the drug in the body (example: 35 hours)

The variable: T: Time (example: 10, 20, 30, 40, 50, ... hours)

And from that, I need the equation to calculate: L: Level of drug in the body

I hope the question is clear enough; if not, I can try to clarify.

PS - yes, the ACTUAL level will differ from the estimate, as there is a gazillion of factors involved, but I just want the estimate. :)

#Biology

Easy Math Editor

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Comments

What have you tried?

How would you model this growth?

Calvin Lin Staff - 5 years, 2 months ago

I have tried using radioactivity formulas, expressing time as fractions of half-lives. That works excellently for the initial dosage.

The model I think could work is to treat it as a heap of radioactive material, that is being added to every 24 hours, but I am not sure how to build the equation around that.

Martin Feigl - 5 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$