Differential Equations Quiz
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APPLICATIONS OF FIRST-ORDER ODES
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A fermentation tank contains 500 liters of nutrient solution. Fresh nutrient with concentration 8 g/L enters at rate Q L/min, while the culture is harvested at rate Q L/min to maintain constant volume. If the microorganisms consume nutrients at a rate proportional to both the nutrient concentration C and the biomass concentration B (where B=2.5 g/L remains constant), with consumption rate constant k=0.15 L/(g·min), what inflow rate Q is needed to maintain C=6 g/L?
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