Teaching and Learning Quantitative Reasoning

**Thinking Quantitatively Project 8**: *Dosage Modeling*

When a drug is administered the amount of the drug in the subject’s blood stream quickly spikes up, then slowly decreases as the body naturally absorbs and excretes it.

- Make a sketch of the graph of the amount of a drug in the bloodstream over time. Don’t worry about specific numbers; we are interested in the pattern of increase and decrease.

- Suppose that a patient is given doses of 100 milligrams of an antibiotic every 12 hours, and that the body removes the medication at the rate of 80% every twelve hours. Make a spreadsheet/sequence that describes the amount of the antibiotic in the bloodstream at 12-hour intervals over a seven day period.

- Graph the amount of antibiotic over this time period.

- Does it look like what you expected?

- It is clearly desirable to have the peaks and valleys of the graph not be too extreme; that is, we may not want the subject swinging between very high and very low amounts of the medication. One way to smooth the graph out a bit is to apply smaller doses at shorter intervals. Modify your spreadsheet/sequence to reflect 50 mg doses every six hours,

- and then 25 mg every three hours.

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