### Penicillin clearance model exercise answers

Here we give answers to some of the exercises on penicillin clearance..

#### Exercise 1

$$A_t = 2 \times 0.95^t, \qquad A_{20} = 0.717$$

#### Exercise 2

\begin{align*} S_{t+1} - S_t & = \text{Amount added to serum} - \text{Amount removed from serum} \\ & = 0.10 I_t \quad - \quad 0.15 \times S_t \end{align*}

#### Exercise 3

a. $P_t \approx 71 \times 0.78^t $

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