Problem 70E

70. 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 increases the concentration by $1.5 \mathrm{mg} / \mathrm{L}$.

(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?

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