An antibiotic has a halflife of 36 hours. If a patient takes on 10 mg tablet every 24 hours. What are the highest and lowest amounts of antibiotic that will be in the patient's body every 24 hours after the patient has taken the drug a long time? Can you write equations for the 1) highest and 2) lowest levels of the drug the patient experiences as a function of the number of days the patient has been taking the antibiotic? My paperwork got accidentally thrown away but I approximated a peak level fo about 35 mg, though I think I was a little off.

## math for fun

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Edited: Jun 27, 2020

# A pharmacologist friend of mine asked me an interesting real-world question.

A pharmacologist friend of mine asked me an interesting real-world question.

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Thank you very much. I think your solution is correct. It was a better approach than I took and I realized I made a mistake and accidentally doubled my final answer. I had written out a long reply but for some reason it didn't repost to hear. I hope this much shorter reply does

Is anybody home?

Good problem. I came up with the infinite series first but added the table to show how y0 changes each day. There's probably some fancy name for this variation of exponential growth but I don't know it. Asymptotic is the correct term rather than maximum value. Thanks again.