Math 12AP – Exponents and Logarithms Review
The Equations!
|
General Form |
Transformational
Form |
|
|
|
|
a = initial
value of the function (... the y-intercept of the graph) b = the
common ratio
c = time
to change by the common ratio d = the horizontal
asymptote |
VS =
vertical stretch VT =
vertical translation b = common
ratio HS =
horizontal stretch. If HS < 0, then
the graph will change from growth to decay (or decay to growth if 0 < b
< 1) HT =
horizontal translation |
The Shape of an
Exponential Function - The terms of arithmetic sequence form a
linear function. The graph of this
linear function will be a straight line.
The terms of a geometric sequence form an exponential function. The graph of an exponential function will be
a curved line that gets steeper and steeper.
Exponential Growth (e.g. 
). The first graph, , shows exponential growth.
Exponential growth can be used to model functions like nuclear
reactions, population growth, and investment growth.
Exponential Decay (e.g. 
). The second graph, , shows exponential decay.
Exponential decay can be used to model functions like carbon-14 dating
and depreciation of car values.
Exponent Rules
- Multiplication
Law
- Division
Law
- Power
of a Product
- Power
of a Quotient
- Power
of a Power
- Negative
Exponents
- Zero
Exponents
, provided x
≠ 0 - Exponentiation
for Rational Exponents
Logarithms - A logarithm is the inverse operation of an exponent. That means that whatever an exponent does, a logarithm with “undo.” The argument of a logarithm can never be a negative number.
Logarithms Rules
- Logarithm
of a Product:
- Logarithm
of a Quotient:
- Logarithm
of a Power:
- Change
of Base formula:
