Exponentials
An exponential curve is any curve of the form
Examples are given below.
Black:
Red:
Blue:
All exponential curves
have the property of passing through the point
whatever the value of
There is a very special number, labelled
called the natural base.
is labelled
.
Typically we have to solve equations of the form:
If we substitute
we obtain the normal quadratic equation
which we can solve using either the quadratic formula or factorising and solving. The equation above factorises as
so we solve
to obtain
Example: Solve
Again we substitute, this time,
The above equation becomes
This factorises into
so we solve
to obtain
There is no real value of
so the only solution here is
