AQA A Level Maths: Pure复习笔记6.3.3 Using Log Graphs in Modelling

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”

6.3.3-Using-Log-Graphs-in-Modelling-Notes-fig3

  • Plotting ln y against t produces a straight line

6.3.3-Using-Log-Graphs-in-Modelling-Notes-fig2

  • 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

6.3.3-Using-Log-Graphs-in-Modelling-Notes-fig4

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

6.3.3-Using-Log-Graphs-in-Modelling-Notes-fig5 6.3.3-Using-Log-Graphs-in-Modelling-Notes-fig6 6.3.3-Using-Log-Graphs-in-Modelling-Notes-fig7 6.3.3-Using-Log-Graphs-in-Modelling-Notes-fig8

Worked Example

6.3.3-Using-Log-Graphs-in-Modelling-Example-fig2

6.3.3-Using-Log-Graphs-in-Modelling.-Example-fig3

 

 

 

 

 

 

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