These are the statements describing what students need to learn:
- know and use the function ax and its graph, where a is positive. Know and use the function ex and its graph
- know that the gradient of ekx is equal to kekx and hence understand why the exponential model is suitable in many applications
- know and use the definition of logax as the inverse of ax, where a is positive, not equal to 1 and x ≥ 0.Know and use the function ln x and its graph. Know and use ln x as the inverse function of ex
- understand and use the laws of logarithms:
logax + logay = loga(xy)
logax − logay = loga(x÷y)
klogax = logaxk
(including, for example,k = −1 and k = −½) - Solve equations of the form ax = b
- use logarithmic graphs to estimate parameters in relationships of the form y = axn and y = kbx, given data for x and y
- understand and use exponential growth and decay; use in modelling (examples may include the use of e in continuous compound interest, radioactive decay, drug concentration decay, exponential growth as a model for population growth); consideration of limitations and refinements of exponential models
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