Exponential Growth (PowerPoint) by pengxuezhi


									Lesson 8.1

Exponential Growth
 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
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:
                      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
A) Annually

B) Monthly

C) Daily

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