Environmental Microbiology

Microbial Growth Kinetics

Exponential growth, generation time and the Monod model — the microbiology that drives biological treatment.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Under unlimited substrate, microbial populations grow exponentially: the number doubles every generation (doubling) time. When substrate limits growth, the specific growth rate follows the Monod equation, saturating at

μ_{ma x}

. The growth curve has lag, exponential (log), stationary and death phases.

The Core Formula Matrix

Exponential growth:

N = N_{0} 2^{t / t_{g}}

(

t_{g}

= generation time)

Specific growth rate:

μ = \frac{ln 2}{t _{g}}

Monod model:

μ = μ_{ma x} \frac{S}{K _{s} + S}

(

S

= substrate,

K_{s}

= half-saturation constant)

Phases: lag → exponential (log) → stationary → death.

The ‘IIT Traps’

⚠
**At $S = K_{s}$ , $μ = μ_{ma x} /2$ ** — that is the definition of the half-saturation constant.
⚠
Generation time is constant only during the exponential phase.
⚠
Use base-2 for doublings but base-e for the specific growth rate.

📚 Standard references

Environmental Microbiology — Ian L. Pepper, Charles P. Gerba & Terry J. Gentry
Brock Biology of Microorganisms — Madigan et al.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · NAT

A bacterial culture has a generation (doubling) time of 30 min. Starting from one cell, after 3 hours the number of cells is _____.

Q2MEDIUM2 Marks · MCQ

In the Monod equation, when the substrate concentration

S

equals the half-saturation constant

K_{s}

, the specific growth rate

μ

is:

Q3HARD2 Marks · MCQ

The phase of the bacterial growth curve in which the death rate balances the growth rate, giving a constant viable population, is the: