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## 'Drug Stabiliser' printed from http://nrich.maths.org/

### Why do this problem?

This problem gives an interesting insight into basics of drug
administration and consider how altering the dosage given affects
the levels of a drug in the body. It gives a good application of
the concept of exponential decay in a way that does not need to be
algebraic but gives a greater appreciation of the nature of these
formulae in numerical terms.

### Possible approach

This problem would work well as a homework exercise followed up by
a class discussion of the problem. The concepts required are not
complex but may involve some in depth reasoning. It might be a good
idea to ask students to explain their reasoning and discuss some of
the latter problems in class if they prove too tricky.

### Key questions

- How does the level of a drug in the body vary depending on its
half-life?
- How does the question of when the drug is administered affect
the minimum and maximum levels of the drug in the body?
- Can you represent your thoughts in an algebraic form that makes
calculations easier?

### Possible extension

Can students plot the relationships that they find in
graphical form?

What possible effects could very large doses of certain drugs
administered weekly to attain the same minimum drug level as a
daily dose have on a patient?

What if a drug breaks down into another physiologically active
compound? How would this impact on the level of drug derived active
compounds if a daily dose is given?

Can you think of any other scenarios where similar patterns of
decay are observed?

### Possible support

The worked solution should offer a great degree of support. Some
background information on the mathematics of exponential decay
would be useful in completing this problem. Graphs of decay
relationships may help conceptual understanding.