exponential function

A function of the form
f (x) = a
^{x}
where
a
is any positive constant except 1.
inverse function

The inverse,
f
^{1}(x)
, reverses the operations of
f (x)
. If
f
^{1}(x)
exists for a
certain function
f
, then
f (f
^{1}(x)) = x
and
f
^{1}(f (x)) = x
.
logarithmic differentiation

A method of finding the derivatives of functions that are raised to powers of the variable
x
. The use of logarithms helps to convert powers into products, which are more
readily differentiated.
exponential growth

A type of growth in which the rate of change of the quantity is proportional to the
quantity itself. In other words,
= ky


Functions with this property have a constant percentage increase per time interval, and
are of the form
With exponential growth,
k
is greater than zero.
exponential decay

A type of decay in which the rate of change of the quantity is proportional to the quantity
itself. In other words,
= ky


Functions with this property have a constant percentage decrease per time interval, and
are of the form
With exponential decay,
k
is less than zero.