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Using Log Graphs in Modelling (CIE A Level Maths: Pure 3)
Revision Note
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=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
Worked example
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