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

How fast does my heart rate recover after exercise?

AA SLAI SLAA HLAI HL Accessible Also in: Modelling, Sport

Research question

Does my heart rate after a standard exercise test decay exponentially towards my resting rate, and does the fitted recovery constant improve over six weeks of training?

Make it yours, then agree it with your teacher.

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Why it makes a good exploration

Heart-rate recovery is used as a fitness indicator. Logging your own recovery with a watch or chest strap and fitting an exponential model gives personal, repeatable data and a real question about your training.

The mathematics you'll need

Exponential decay to an asymptote
Linearising with logarithms
Comparing fitted constants over time
Residuals and the early fast phase

Modelling the data, step by step

This idea usually needs an exponential model. See it worked step by step, with a criterion tip at every step: Exponential y = a e^(kx) + c and y = a·bˣ · Choosing and comparing models.

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

Record heart rate every 10 s for 5 minutes after a fixed exercise test, weekly for six weeks.

phyphox (RWTH Aachen) — Free app that turns your phone's accelerometer, microphone, barometer and gyroscope into data loggers with CSV export.

A possible outline

Describe the test protocol precisely.
Fit the exponential model each week.
Compare the recovery constant over time.
Check whether a two-phase model fits better.
Reflect on sleep, caffeine and device accuracy.

Pitfalls that cost marks

Changing the test protocol between weeks.
Wrist sensors lag behind real heart rate — mention it.
Only one test per week without repeats.

Showing personal engagement

It is your own data — describe how the training felt.
Compare with a friend who does not train.
Predict your week-six constant before measuring.

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 decay to an asymptote; Linearising with logarithms
AA HL	Fits, but add an HL technique	Exponential decay to an asymptote; Linearising with logarithms
AI SL	Good fit	Exponential decay to an asymptote; Linearising with logarithms
AI HL	Fits, but add an HL technique	Exponential decay to an asymptote; Linearising with logarithms

Level: Accessible. A good first extended piece of maths, with room to go deeper. 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: changing the test protocol between weeks; and wrist sensors lag behind real heart rate — mention it. Say how each one affects your answer.

Use of mathematics (E)

SL: exponential decay to an asymptote; linearising with logarithms; comparing fitted constants over time; residuals and the early fast phase, 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 a two-exponential model (fast and slow recovery) and compare with the single exponential.

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, AI SL, AA HL and AI HL. We rate it Accessible: a good first extended piece of maths, with room to go deeper.

What mathematics does this IA use?

Exponential decay to an asymptote, linearising with logarithms, comparing fitted constants over time and residuals and the early fast phase.

Where can I get data for this IA?

Record heart rate every 10 s for 5 minutes after a fixed exercise test, weekly for six weeks. Checked sources and tools: phyphox (RWTH Aachen).

Turn this idea into your IA

The planner opens with “How fast does my heart rate recover after exercise?” filled in: the question, the maths and the data sources.

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