IB Maths AI 2.8 Definitions

This page contains our IB Maths AI definitions for 2.8. By learning each one of these definitions, you will fully cover the content for IB Maths AI 'Logarithmic graphs'.

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

exponential model

A model of the form

y=ab^x

; taking logarithms gives

\log y=\log a+x\log b

, which is linear in

x

gradient

The coefficient

a

y=ax+b

, giving the predicted change in

y

when

x

increases by

1

intercept

The value where a straight line crosses the vertical axis; in the linearized forms it equals

\log a

linear scale

An axis scale with equal spacing for equal differences in value.

linearization

Transforming a curved relationship into a straight-line form by taking logarithms, so that a best-fit straight line can be used to estimate model parameters.

log-log graph

A graph with both axes on logarithmic scales; used to test for power relationships by plotting

$\log y$ against

$\log x$ .

logarithmic

Based on logarithms, so equal distances on an axis represent equal ratios (multiplicative changes) rather than equal differences.

logarithmic scale

An axis scale that increases by equal ratios; for example, values like

1

10

100

, and

1000

are equally spaced because each is

10

times the previous value.

power model

A model of the form

y=ax^n

; taking logarithms gives

\log y=\log a+n\log x

, which is linear in

\log x

semi-log graph

A graph with one axis on a logarithmic scale and the other on a linear scale; used to test for exponential relationships by plotting

$\log y$ against $x$ .

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