Running away from a tiny monster

You've become infected by the newly discovered bacterium Diarrhea ultradanger. The mode by which D. ultradanger attacks the body is by producing a harmful type of molecule called enterotoxin.

As a defense, your doctor prescribes you the antibiotic medicine chloramphenicol which reaches a concentration \(c_0\) in the bloodstream upon administration. However, being a highly successful pathogen, D. ultradanger can destroy molecules of chloramphenicol by producing the enzyme chloramphenicol acetyltransferase (CAT) and exporting it into the bloodstream. If D. ultradanger can manage to keep CAT at the concentration \(c_0\) in the bloodstream, it will escape the drug treatment and cause awful diarrhea. As a further counteraction, the body can degrade molecules of CAT at a rate \(\beta_\text{deg}\).

If \(\beta_\text{deg} = 5 \text{ s}^{-1}\), and \(c_0 = 17 \text{ mM}\), what is the minimum rate (in \(\text{mM/s}\)) at which the D. ultradanger cells must produce CAT in order to escape the drug treatment?

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