Modelling bacterial growth in the biology lab

AA SLAA HLAI SLAI HL Solid Also in: Modelling, Differential equations

Research question

Does the growth of a harmless bacterial culture (measured by optical density or colony counts) follow a logistic model, and what doubling time does the exponential phase give?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Growth curves have distinct phases — lag, exponential, stationary. With your biology department's help, you can collect real microbiology data and model it properly.

The mathematics you'll need

Exponential and logistic functions
Log-linear regression for the exponential phase
Doubling time
Piecewise modelling of phases

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Work with your biology teacher using a safe organism and standard lab methods; record measurements at regular intervals.

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Describe the lab procedure and safety.
Identify phases in the data.
Fit the exponential phase and a logistic model.
Compare with published doubling times for the organism.
Reflect on measurement error and temperature control.

Pitfalls that cost marks

Unsafe or unsupervised microbiology — always work with a teacher.
Fitting one model to all phases without discussion.
Too few time points.

Showing personal engagement

Link to your Biology IA if appropriate (without reusing work).
Compare two temperatures.
Explain the lag phase in your own words.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Fit the Gompertz model (explain it) and compare with the logistic.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).