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Exponentials

An exponential curve is any curve of the formExamples are given below.

Black:

Red:

Blue:

All exponential curveshave the property of passing through the pointwhatever the value ofThere is a very special number, labelledcalled the natural base.is labelled.

Typically we have to solve equations of the form: If we substitute we obtain the normal quadratic equationwhich we can solve using either the quadratic formula or factorising and solving. The equation above factorises asso we solveto obtain

Example: Solve

Again we substitute, this time,The above equation becomesThis factorises intoso we solveto obtain

There is no real value ofso the only solution here is

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