CIE A Level Maths: Pure 3复习笔记2.3.3 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

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

• Plotting ln y against t produces a straight line

• 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

How do I use a logarithmic graph with exponential modelling?

• Exponential models are of the form
  • y=Ab^kx (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