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# A patient is injected with a drug every 12 hours. Immediately before each injection the concentration of the drug has been reduced by $90\%$ and the new dose in increase the concentration by 1.5 mg/L. (a) What is the concentration after three doses?(b) If $C_n$ is the concentration after the $n$th dose, find a formula for $C_n$ as a function of $n.$(c) What is the limiting value of the concentration?

## (A). 1.665 $\mathrm{mg} / \mathrm{L}$(B). $C_{n}=\frac{5}{3}\left[1-0.1^{n}\right]$(C). $\frac{5}{3} \mathrm{mg} / \mathrm{L}$

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##### Catherine R.

Missouri State University

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Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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