IA idea · Differential equations & dynamics

How does bread dough rise? A logistic model in the kitchen

AA SLAA HLAI SLAI HL Accessible Also in: Modelling, Health & biology

Research question

Does the volume of rising bread dough follow a logistic curve, and how do the growth rate and maximum volume change with temperature?

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

Why it makes a good exploration

Yeast grows quickly and then runs out of sugar and space — a textbook logistic process you can measure with a jar, a ruler and a timer. Changing the temperature gives a real comparison.

The mathematics you'll need

Logistic function and its parameters
Fitting by technology and interpreting parameters
Comparing with exponential growth early on
HL: the logistic DE and its solution

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

Put equal dough portions in straight-sided jars at 2–3 temperatures and record height every 10 minutes for 3 hours (time-lapse helps).

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

Explain why growth should be logistic.
Collect heights at different temperatures.
Fit logistic models; compare with exponential for early data.
Compare fitted growth rates across temperatures.
Reflect on collapse after the peak and measurement from the meniscus.

Pitfalls that cost marks

Jars with sloping sides (height is not proportional to volume).
Inconsistent dough portions.
Fitting only the early part of the curve.

Showing personal engagement

Bake with a family recipe and explain its proving time using your model.
Predict the best proving temperature and test it.
Compare fresh and dried yeast.

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

Taking it further

Estimate the doubling time of the yeast population from the early exponential phase.

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).