8 1 Exponential Growth - PowerPoint by ps1z0u

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									8.1 Exponential Growth

        p. 465
    Exponential Function
• f(x) = bx where the
  base b is a positive
  number other than
  one.
• Graph f(x) = 2x
• Note the end
  behavior
• x→∞ f(x)→∞
• x→-∞ f(x)→0
• y=0 is an asymptote
            Asymptote
• A line that a graph approaches as you move
  away from the origin
                            The graph gets closer
                            and closer to the line
                            y = 0 …….
                            But NEVER reaches it


                              2 raised to any power
                              Will NEVER be zero!!

                 y=0
Lets look at the activity on p. 465


 • This shows of y= a * 2x
 • Passes thru the point (0,a) (the y
   intercept is a)
 • The x-axis is the asymptote of the graph
 • D is all reals (the Domain)
 • R is y>0 if a>0 and y<0 if a<0
 • (the Range)
• These are true of:
• y = abx
• If a>0 & b>1 ………
• The function is an
  Exponential Growth Function
                Example 1
• Graph y = ½ 3x
• Plot (0, ½) and (1,
  3/2)
• Then, from left to
  right, draw a curve
  that begins just
  above the x-axsi,
  passes thru the 2
  points, and moves
  up to the right
D+
     D= all reals
     R= all reals>0




                        y=0


           Always mark asymptote!!
               Example 2
• Graph y = - (3/2)x
• Plot (0, -1) and
  (1, -3/2)                y=0
• Connect with a
  curve
• Mark asymptote
• D=??
• All reals
• R=???
• All reals < 0
To graph a general Exponential
          Function:
• y = a bx-h + k
• Sketch y = a bx
• h= ??? k= ???
• Move your 2 points h units left or right
  …and k units up or down
• Then sketch the graph with the 2 new
  points.
           Example 3
        Graph y = 3·2x-1-4

• Lightly sketch y=3·2x
• Passes thru (0,3) &
  (1,6)
• h=1, k=-4
• Move your 2 points
  to the right 1 and
  down 4
• AND your
  asymptote k units (4
  units down in this
  case)
D= all reals
R= all reals
       >-4




               y = -4
          Now…you try one!
• Graph y= 2·3x-2 +1
• State the Domain and
  Range!
• D= all reals
• R= all reals >1
                             y=1
          Compound Interest

•A=P(1+r/n)nt
•   P - Initial principal
•   r – annual rate expressed as a decimal
•   n – compounded n times a year
•   t – number of years
•   A – amount in account after t years
   Compound interest example
• You deposit $1000 in an account that
  pays 8% annual interest.
• Find the balance after I year if the
  interest is compounded with the given
  frequency.
• a) annually b) quarterly      c) daily
A=1000(1+ .08/1)1x1 A=1000(1+.08/4)4x1 A=1000(1+.08/365)365x1
 = 1000(1.08) 1      =1000(1.02)4       ≈1000(1.000219)365
                                        ≈ $1083.28
 ≈ $1080             ≈ $1082.43
Assignment

								
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