# Answer to Question #41106 in Differential Equations 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.

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.

Expert's answer

Unfortunately, your question requires a lot of work and cannot be done for free. Please submit it with all requirements as an assignment to our control panel and we'll assist you.

Need a fast expert's response?

Submit orderand get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

## Comments

## Leave a comment