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Answer on Differential Equations Question for sam

Question #41106
Mathematical modeling of an experiment: two competing bacterial strains,
x1 and x2, growing in a chemostat where nutrient, S, is supplied at input
concentration S0.
We know that

(a) at low nutrient concentration the rate of uptake and bacteria growth is
limited by, and proportional to, nutrient concentration,

(b) at high concentration the uptake and bacterial growth rates saturate and
become constant, independent of nutrient concentration.
This type update and growth kinetics is typically described by Michaelis-
Menten kinetics:
dx1/dt = alpha1 (x1 S /(a1 + S))

1. 1. Draw a simple diagram of the conceptual model
2. Write the differential equations for bacteria x1, x2, and nutrient S.
3. add bacteria x2 killing x1 as additional food: diagram +
equations.
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