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These are the statements describing what students need to learn:

- know and use the function a
^{x}and its graph, where a is positive. Know and use the function e^{x}and its graph - know that the gradient of e
^{kx}is equal to ke^{kx}and hence understand why the exponential model is suitable in many applications - know and use the definition of log
_{a}x as the inverse of a^{x}, 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 e^{x} - understand and use the laws of logarithms:

log_{a}x + log_{a}y = log_{a}(xy)

log_{a}x − log_{a}y = log_{a}(x÷y)

klog_{a}x = log_{a}x^{k}

(including, for example,k = −1 and k = −½) - Solve equations of the form a
^{x}= b - use logarithmic graphs to estimate parameters in relationships of the form y = ax
^{n}and y = kb^{x}, 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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