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

Is solar power growing logistically?

AA SLAA HLAI SLAI HL Solid Also in: Modelling, Finance

Research question

Is the share of electricity from solar in [a country] better described by an exponential or a logistic model, and what saturation level does the logistic model suggest?

Make it yours, then agree it with your teacher.

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Why it makes a good exploration

New technologies often spread along S-curves. Ember's electricity data lets you test whether solar is still in its exponential phase or already slowing — with a real policy question at the end.

The mathematics you'll need

Exponential and logistic models
Fitting with technology and interpreting parameters
Doubling time
Out-of-sample testing

Modelling the data, step by step

This idea usually needs exponential or logistic 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)).

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

Yearly generation by source from Ember's electricity data.

Ember electricity data — Yearly generation by source, emissions and capacity for 200+ countries (CC BY 4.0).

Real data for this idea

Readable chart: Our World in Data: Electricity generation (share of generation from renewables). Use it to see the pattern; download your numbers from the primary source or the chart's own download. Cite as: Our World in Data, ‘Electricity generation’, CC BY 4.0. Original source: Ember (2026) and other sources.

The chart's download carries Ember's yearly electricity data (CC BY 4.0): cite Ember as the original source. Links checked October 2026; we link to the data and never copy it. More free data sets.

A possible outline

Explain why adoption might be logistic.
Fit both models to early years.
Compare predictions with recent years.
Interpret the saturation level.
Reflect on policy, storage and grid limits.

Pitfalls that cost marks

Fitting a logistic before the inflection point (very unstable).
Ignoring changes in total demand.
Undated data.

Showing personal engagement

Choose your own country and a contrasting one.
Compare solar and wind.
Relate to solar panels you see locally.

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 models; Fitting with technology and interpreting parameters
AA HL	Good fit	Exponential and logistic models; Fitting with technology and interpreting parameters
AI SL	Good fit	Exponential and logistic models; Fitting with technology and interpreting parameters
AI HL	Good fit	Exponential and logistic models; Fitting with technology and interpreting parameters

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: fitting a logistic before the inflection point (very unstable); and ignoring changes in total demand. Say how each one affects your answer.

Use of mathematics (E)

SL: exponential and logistic models; fitting with technology and interpreting parameters; doubling time; out-of-sample testing, each explained in your own words and carried out correctly.

How environment explorations reach the top bands in general: Environment & climate IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

Investigate how the fitted saturation level changes as each new year of data is added.

Extending it for HL

Add an HL technique the question genuinely needs: what an HL environment exploration adds.

See a complete IA, marked

When can we launch? Modelling the tide at our sailing club's slipway (AA SL) is a complete environment 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 models, fitting with technology and interpreting parameters, doubling time and out-of-sample testing.

Where can I get data for this IA?

Yearly generation by source from Ember's electricity data. Checked sources and tools: Our World in Data and Ember electricity data.

Turn this idea into your IA

The planner opens with “Is solar power growing logistically?” filled in: the question, the maths and the data sources.

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