Using Log Graphs in Modelling (CIE A Level Maths: Pure 3)

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Using Log Graphs in Modelling

What are log graphs?

  • Log graphs are used when the scale of a graph increases or decreases exponentially
  • It can very difficult to read specific values from graphs with these scales

6-3-3-using-log-graphs-in-modelling-notes-fig1_1

 

  • Taking ln of both sides allows the equation to be rearranged into the form “y = mx + c

Using Log Graphs in Modelling Notes fig3, A Level & AS Maths: Pure revision notes

  • Plotting ln y against t produces a straight line

Using Log Graphs in Modelling Notes fig2, A Level & AS Level Pure Maths Revision Notes

  • Note the second graph has ln y on the y-axis
    • Log graphs have at least one logarithmic axis
  • Reading a value for ln y at t = 20 is easier than reading the value for y
  • Logarithmic axes are used where a wide range of numbers can occur
    • it makes numbers smaller and easier to deal with
    • a curve can be turned into a straight line

Using Log Graphs in Modelling Notes fig4, A Level & AS Level Pure Maths Revision Notes

How do I use a logarithmic graph with exponential modelling?

  • Exponential models are of the form
    • y=Abkx (growth)
    • y=Ab-kx (decay)

  • To use a model to make predictions the values of A, b and k are needed
  • A, b and k will usually be estimated from observed data values
    • A may be known exactly, as it is a starting/initial value

  • Estimating from a straight line graph is easier than from a curve

 Using Log Graphs in Modelling Notes fig5, A Level & AS Level Pure Maths Revision Notes Using Log Graphs in Modelling Notes fig6, A Level & AS Maths: Pure revision notes Using Log Graphs in Modelling Notes fig7, A Level & AS Maths: Pure revision notes Using Log Graphs in Modelling Notes fig8, A Level & AS Maths: Pure revision notes

Worked example

Using Log Graphs in Modelling Example fig2, A Level & AS Level Pure Maths Revision Notes

Using Log Graphs in Modelling. Example fig3, A Level & AS Maths: Pure revision notes

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Paul

Author: Paul

Expertise: Maths

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.