Does my phone battery really drain in a straight line?

AI SLAI HLAA SL Accessible Also in: Statistics

Research question

Is my phone's battery percentage over a day of normal use better described by a linear, piecewise-linear or exponential model, and can the best model predict when the phone will die?

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

Why it makes a good exploration

Phones show a percentage and an estimated time left — but how do they estimate it? Logging your own battery and testing models against the phone's prediction is personal, easy to collect and surprisingly subtle.

The mathematics you'll need

Linear and exponential regression
Piecewise functions
Residual analysis and R²
Using a model to predict and comparing with reality

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

Record battery percentage every 15 minutes on three days with similar use (screenshots of the battery graph work), noting screen-on periods.

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

Describe your usage pattern and data collection honestly.
Fit linear and exponential models to day one.
Notice where the fit breaks (heavy use, idle) and build a piecewise model.
Predict day two's shut-down time and compare with what happened.
Reflect on why batteries do not discharge evenly (percentage is estimated, not measured).

Pitfalls that cost marks

Changing usage between days so the models are not comparable.
Using R² alone to pick a model.
Treating the percentage as an exact measurement.

Showing personal engagement

Compare your model's predicted time left with the phone's own estimate.
Run a controlled test (video playing, screen at fixed brightness) to separate usage from the battery itself.
Compare two phones or an old and a new battery.

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

Taking it further

Investigate the voltage–charge curve of lithium-ion cells and explain why the last 20% often falls faster.

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).