Exponential or logistic? Modelling my country's population

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

Research question

Which of an exponential, logistic or polynomial model best fits [country]'s population from 1950 to 2000, and which best predicts the actual population from 2000 to today?

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

Why it makes a good exploration

Population models are a classic for a reason: the choice between exponential and logistic is a real scientific question. Using your own country — and testing predictions on data the model did not see — makes it yours.

The mathematics you'll need

Exponential and logistic functions
Linearising with logarithms
Least-squares regression and residuals
Using a model for out-of-sample prediction
HL: the logistic differential equation dP/dt = kP(1 − P/L)

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

Download the population series for your country from the UN World Population Prospects or Our World in Data.

UN World Population Prospects 2024 — Official UN population estimates 1950–present and projections to 2100, CSV bulk download.
Our World in Data — Clean country-level time series (CO₂, population, health, energy, education) with CSV download on every chart.
World Bank Open Data — Development indicators (GDP, life expectancy, mortality, internet use) for every country, usually from 1960.

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 each model is plausible for population.
Fit each model to 1950–2000 only.
Compare fits and then compare predictions for 2000–present.
Interpret the logistic carrying capacity and compare with UN projections.
Reflect on events (migration, policy, conflict) the models cannot capture.

Pitfalls that cost marks

Fitting to all the data and calling the fit a prediction.
Choosing a high-degree polynomial because R² is higher.
Ignoring that the carrying capacity is very sensitive to the data range.

Showing personal engagement

Choose a country you have a connection to and explain its history.
Compare two countries with different demographic histories.
Compare your prediction with the official UN projection and explain the difference.

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

Taking it further

HL: fit the logistic DE directly with Euler's method, or explore how the fitted carrying capacity changes as you add each decade of data.

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).