Back to: MICROBIOLOGY 400 LEVEL
Welcome to class!
Welcome back, champ! It’s always a pleasure to see your face light up with curiosity and understanding. Today’s lesson is one that combines biology with a little maths, but don’t worry—it’s going to be clear, simple, and very relatable. We’ll be learning about Growth Phases and Mathematical Modelling in microbiology. Let’s make this as easy to understand as telling the story of planting and harvesting maize in a Nigerian farm.
Growth Phases And Mathematical Modeling
When microorganisms like bacteria are placed in a fresh, nutrient-rich environment (like a broth in the lab), they don’t all grow at once. They go through different phases of growth, just like how a baby grows from infancy to adulthood.
There are four major phases in microbial growth:
Lag Phase
This is the adjustment period. The microbes are alive, but they’re not multiplying yet.
Think of a new student arriving at university—they spend time settling in before starting to study.
Log (Exponential) Phase
This is the active growth phase. Microbes multiply very fast—doubling in number at a constant rate.
It’s like a business that finally goes viral and starts getting plenty of customers every hour.
Stationary Phase
Here, growth levels off. Nutrients reduce, and waste increases. Microbes stop multiplying because conditions aren’t so favourable anymore.
Just like a full danfo bus—no one else can enter until someone gets off.
Death (Decline) Phase
Now, the cells begin to die more than they grow because the environment has become too toxic or empty of nutrients.
It’s like food left outside for days—it starts spoiling slowly until it’s no longer useful.
Mathematical Modelling of Microbial Growth
Scientists use maths to describe how fast microbes grow. This helps in planning industrial processes like how much yeast to add when brewing or how long to let bacteria grow in a bioreactor.
The most common model is during the log phase and it’s expressed as:
N = N₀ × 2ⁿ
Where:
N = final number of cells
N₀ = starting number of cells
n = number of generations (how many times they double)
You can also calculate the generation time (time for the population to double):
G = t / n
Where t = total time, and n = number of generations.
This helps industries know how long to run a fermentation process for maximum product yield.
Practical Example
Let’s say a fermentation tank starts with 1,000 bacteria, and they double every 30 minutes. After 3 hours (which is 6 generations), we can calculate:
N = 1,000 × 2⁶ = 1,000 × 64 = 64,000 bacteria
That’s how quickly microbes can multiply when the conditions are right!
Summary
- Microbial growth follows four phases: lag, log, stationary, and death.
- During lag phase, microbes adjust but don’t multiply.
- Log phase is when cells multiply rapidly and can be mathematically modelled.
- Stationary phase shows no net growth, and death phase shows population decline.
- Mathematical models help estimate population size and growth rate in microbial processes.
Evaluation
- List and explain the four phases of microbial growth.
- What does the formula N = N₀ × 2ⁿ represent?
- Why is the log phase important in industrial microbiology?
Today, you’ve not only learned science—you’ve connected biology with numbers, just like real scientists do every day in labs around the world. Keep shining, keep learning, and always remember Afrilearn is proud to support your journey. See you in the next exciting lesson!