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

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