# Exponential Growth (PowerPoint) by pengxuezhi

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```									Lesson 8.1

Exponential Growth
Vocabulary
 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
a decimal.
Example 1: Graphing Functions of the Form y =
abx                               x
1 x                       4
A) y   4              B) y   3 
4                          
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
Function
Describe the translation on:

x 1
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.
Compound Interest

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:
nt
    r 
A  P1    
    n
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
frequency:
A) Annually

B) Monthly

C) Daily

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