In another project for the pharmaceutical company described...

In another project for the pharmaceutical company described in #1, you are in charge of a bacterial culture tank (for antibiotic production), completely sealed off from the environment (but with access ports so one can add or remove material from the tank). Review all of the conditions you must maintain within the culture tank for the bacteria to thrive and produce the antibiotic.

Drug concentration An antibiotic is administered intravenously into the bloodstream at a constant rate $r .$ As the drug flows through the patient's system and acts on the infection that is present, it is removed from the bloodstream at a rate proportional to the amount in the bloodstream at that time. Since the amount of blood in the patient is constant, this means that the concentration $y=y(t)$ of the antibiotic in the bloodstream can be modeled by the differential equation $$\frac{d y}{d t}=r-k y, \quad k>0$$ \begin{equation} \begin{array}{l}{\text { a. If } y(0)=y_{0}, \text { find the concentration } y(t) \text { at any time } t} \\ {\text { b. Assume that } y_{0}<(r / k) \text { and find } \lim _{y \rightarrow \infty} y(t) . \text { Sketch the }} \\ {\text { solution curve for the concentration. }}\end{array} \end{equation}

Transcendental Functions

Exponential Change and Separable Differential Equations

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