sparknotes
Inverse, Exponential, and Logarithmic Functions
Terms for Topic "Inverse, Exponential, and Logarithmic Functions"
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,
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.
 = ky
|
Functions with this property have a constant percentage increase per time interval, and are of the form
| y = y 0 e kt |
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,
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.
|
= ky
|
Functions with this property have a constant percentage decrease per time interval, and are of the form
| y = y 0 e kt |
With exponential decay, k is less than zero.
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