Edexcel A Level (IAL) Biology -6.3 The Bacterial Growth Curve- Study Notes- New Syllabus

Bacterial Growth Curve and Exponential Growth Rate Constant

🌿 Introduction

When bacteria reproduce in a closed culture (like a flask of broth), their population follows a predictable pattern called the bacterial growth curve. It has four phases: lag, exponential, stationary, and death. Understanding these phases helps in predicting population size, planning experiments and calculating growth rates.

1. Lag Phase

What happens in this phase

• Bacteria are adjusting to the new environment.
• Cells prepare for division by synthesising enzymes, proteins and ATP.
• Very little or no cell division occurs.

Why this phase occurs

• Cells may be recovering from stress or damage.
• Nutrient composition is new, so enzymes need to be activated.

2. Exponential (Log) Phase

What happens in this phase

• Cells divide at their maximum rate.
• Population increases exponentially (doubling at constant intervals).
• Conditions are ideal: plenty of nutrients, oxygen and space.

Important point

• This is the phase where growth rate constants and generation time are calculated because growth is most predictable.

3. Stationary Phase

What happens in this phase

• Cell division slows and eventually equals cell death rate.
• Population size becomes stable.
• Nutrients begin to run out and waste products build up.

Why it matters

• Many useful metabolites (e.g., antibiotics) are produced in this phase by some microbes.

4. Death (Decline) Phase

What happens in this phase

• Death rate exceeds cell division.
• Nutrient exhaustion and toxic waste accumulation cause population to decrease.
• Cells may undergo lysis.

How to Calculate Exponential Growth Rate Constant (k)

During the exponential phase, bacterial growth follows this pattern:

\( N = N_0 e^{kt} \)

• \( N_0 \) = initial number of cells
• \( N \) = number of cells after time \( t \)
• \( k \) = growth rate constant
• \( t \) = time (usually hours)

Formula for k

\( k = \frac{\ln N – \ln N_0}{t} \)

This tells you how fast the bacteria are growing.

Generation Time (g)

\( g = \frac{\ln 2}{k} \)

Shorter generation time = faster-growing bacteria.

📌Worked Example:

A culture increases from 2 × 10⁶ cells to 3.2 × 10⁷ cells in 4 hours. Find k.

\( k = \frac{\ln(3.2 \times 10^7) – \ln(2 \times 10^6)}{4} \)

\( k = \frac{\ln(16)}{4} \)

\( k = \frac{2.7726}{4} = 0.693\ \text{h}^{-1} \)

(Recognise \( \ln(16) = 2.7726 \))

Generation time:

\( g = \frac{\ln 2}{k} = \frac{0.693}{0.693} = 1\ \text{hour} \)

📋 Summary Table

Quick Recap 
Four phases: Lag → Exponential → Stationary → Death.
Exponential phase is used to calculate k and generation time.
Growth formula: \( N = N_0 e^{kt} \).
Growth rate constant: \( k = \frac{\ln N – \ln N_0}{t} \).
Generation time: \( g = \frac{\ln 2}{k} \).