Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

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?

Make it yours, then agree it with your teacher.

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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

Modelling the data, step by step

This idea usually needs exponential, logistic, piecewise or straight-line models. See it worked step by step, with a criterion tip at every step: Exponential y = a e^(kx) + c and y = a·bˣ · Logistic y = L/(1 + C e^(−kx)) · Piecewise models · Straight line y = mx + c.

Model your own data Paste it from Desmos, GeoGebra or a spreadsheet and get the same play-by-play with your numbers. New to modelling? Start with the modelling workflow. Writing it up? The IA modelling planner comments on each paragraph as you draft — it never writes it for 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.

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.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Good fit	Exponential and logistic functions; Log-linear regression for the exponential phase
AA HL	Good fit	Exponential and logistic functions; Log-linear regression for the exponential phase
AI SL	Good fit	Exponential and logistic functions; Log-linear regression for the exponential phase
AI HL	Good fit	Exponential and logistic functions; Log-linear regression for the exponential phase

Level: Solid. Needs some independent work beyond class examples. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: unsafe or unsupervised microbiology — always work with a teacher; and fitting one model to all phases without discussion. Say how each one affects your answer.

Use of mathematics (E)

SL: exponential and logistic functions; log-linear regression for the exponential phase; doubling time; piecewise modelling of phases, each explained in your own words and carried out correctly.

How health & biology explorations reach the top bands in general: Health, biology & medicine IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

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

Extending it for HL

Add an HL technique the question genuinely needs: what an HL health & biology exploration adds.

See a complete IA, marked

Is it cheaper to leave the heating on low overnight? A two-temperature model of my bedroom (AI HL) is a complete health & biology exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AA SL, AA HL, AI SL and AI HL. We rate it Solid: it needs some independent work beyond class examples.

What mathematics does this IA use?

Exponential and logistic functions, log-linear regression for the exponential phase, doubling time and piecewise modelling of phases.

Where can I get data for this IA?

Work with your biology teacher using a safe organism and standard lab methods; record measurements at regular intervals. Checked sources and tools: Desmos graphing calculator.

Turn this idea into your IA

The planner opens with “Modelling bacterial growth in the biology lab” filled in: the question, the maths and the data sources.

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