Exponential Function: a function that involves the
expression bx where the base b is a positive
number other than 1.
Asymptote: a line that a graph approaches as you
move away from the origin.
Exponential Growth Function: a function of the
form f(x) = abx where a > 0 and b > 1.
Growth Factor: the quantity 1 + r in the exponential
growth model y = a(1 + r)t where a is the initial
amount and r is the percent increase expressed as
Example 1: Graphing Functions of the Form y =
1 x 4
A) y 4 B) y 3
General Exponential Function
To graph a general exponential
function, y = abx-h +k, begin by
sketching the graph of y = abx. Then
translate the graph horizontally by h
units and vertically by k units.
Example 2: Graphing a General Exponential
Describe the translation on:
A) y 2 3 3
B) y 2 3 x 2 1
Example 3: Modeling Exponential Growth
A) In the past 10 years, an initial population of 44
deer in a state park grew by about 8% per year.
Write a model giving the number d of deer after t
years. About how many deer were in the park
after 5 years?
B) In 1980 about 2,180,000 U.S. workers worked at
home. During the next 10 years, the number of
workers working at home increased 5% per year.
Write a model giving the number w (in millions) of
workers working at home t years after 1980.
Consider an initial principal P deposited in an
account that pays interest at an annual rate r
(expressed as a decimal) compounded n times
per year. The amount A in the account after t
years can be modeled by the equation:
Example 4: Finding the Balance in an Account
You deposit $1400 in an account that pays 4%
annual interest. Find the balance after 1 year if
the interest is compounded with the given