Monod’s Equation is a Mathematical Model for the Growth of Bacteria and other Microorganisms: Mathematical Applications In Biology Assignment, PSB Academy, Singapore

(MAT1MAB)

Monod’s Equation is a mathematical model for the growth of bacteria and other microorganisms.

µ(S) = µmax∗ S/KS + S

• µ(S) is the specific growth rate of the microorganisms
• µmax is the maximum specific growth rate of the microorganisms
• S is the concentration of the limiting substrate for growth
• KS is a constant which depends on the species and the substrate

In the following question, µmax = 0.037 and KS = 0.025, and µ(S) has been calculated to 4 decimal places. Units for the quantities have not been included.

S µ(S)
0 0.0000
0.02 0.0164
0.04 0.0228
0.06 0.0261
0.08 0.0282
0.10 0.0296
0.12 0.0306

S µ(S)
0.14 0.0314
0.16 0.0320
0.18 0.0325
0.20 0.0329
0.25 0.0336
0.30 0.0342
0.35 0.0345

S µ(S)
0.40 0.0348
0.45 0.0351
0.50 0.0352
0.55 0.0354
0.60 0.0355
0.65 0.0356
0.70 0.0357

1. Carefully plot a continuous graph of the data above

2. Calculate the value of µ(0.025). Give your answer correct to 4 decimal places.

3. What is special about the value of µ(0.025)?

4. Which symbols in Monod’s equation are constants?

5. What is the independent variable in Monod’s equation?

6. What is the dependent variable in Monod’s equation?

7. Which of the following statements best describes the function µ(S):
(a) µ(S) is a power function.
(b) µ(S) is an exponential function.
(c) µ(S) is a logarithmic function.
(d) µ(S) is a linear function.
(e) None of the above.

8. Rearrange the equation: µ = µmax∗ S /KS + S so that S is a function of µ. Show each step of your work.

9. Use your answer to question 8 and the values for µmax and KS were given above to find the concentration S such that µ = 0.02. Give your answer correct to 4 decimal places.