IB Maths AI 2.3 Notes

This page contains our IB Maths AI notes for 2.3. By reading each one of these notes, you will fully cover the content for IB Maths AI 'Introduction to modelling functions'.

All Topic 2 Sub-topics 2.1: Forms Of Lines 2.2: Introduction To Functions 2.3: Introduction To Modelling Functions 2.4: Modelling Applications (HL)2.5: Further functions (HL)2.6: Graph transformations (HL)2.7: Advanced modelling functions (HL)2.8: Logarithmic graphs

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Chapters

1. Modelling functions

2. Linear models

3. Quadratic models

4. Exponential growth & decay models

5. Direct & inverse variation

6. Cubic models

7. Sinusoidal models

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Modelling functions

In this section, we look at common function types and how they can be used to model real situations.

A model is a mathematical rule that describes how one quantity depends on another.

Different shapes of graphs are suited to different kinds of behaviour, so choosing the right model helps us interpret data and make predictions.

A good model should match the behaviour of the situation being described.

A linear model is suitable when the rate of change is constant.
A quadratic model is suitable when there is a turning point.
An exponential model is suitable when change happens by a constant percentage or ratio.
A variation model is suitable when one quantity depends on a power of another.
A cubic model is suitable when the graph may change direction more than once.
A sinusoidal model is suitable when the pattern repeats regularly.

In practice, technology is often used to sketch graphs, find roots, and check whether a chosen model fits a given set of data.

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