exponential functions graphs of exponential functions the natural base

Document Sample
exponential functions graphs of exponential functions the natural base Powered By Docstoc
					  Section 3-1


        Exponential and Logistic Functions




Section 3-1

  exponential functions
  graphs of exponential functions
  the natural base e
  logistic functions
  graphs of logistic functions
  population models




                                             1
Exponential Functions

  standard form for an exponential function
               f ( x) = a ⋅ bx
  a is the initial value, b is the base
  b must be positive and not equal to 1
  if b > 1 then its exp. growth
  if 0 < b < 1 then its exp. decay




 Find the exp. function that passes through (0 , 4)
 and (1 , 12)




                                                      2
Graphs
  the basic exponential function graph passes
 through (0 , a) and has a horizontal
 asymptote at y = 0
  growth (b > 1)



 decay (0 < b < 1)




Graphs

  the basic exponential      Try these on your
 function can be             calculator:
 stretched, reflected, and   y=2x
 translated as we
 previously learned.         y=-2x
                             y=2-x

                   x−        y=2x-2
  f ( x) = a ⋅ b        +
                             y=2x-2
                             Y=3(2)x




                                                 3
 Sketch the graph : f ( x ) = 3 ⋅ 2 x −2




The Natural Base e

 one of the basic twelve functions introduced
 in Chapter 1 was f ( x) = e x
 e is known as the natural base e ≈ 2 . 72
 the definition of e:
                                x
                       1
           e = lim  x + 
               x→ ∞
                       x




                                                4
Sketch the graph : f ( x ) = 3 ⋅ e − x




Sketch the graph : f ( x ) = −4 ⋅ (0.3) x + 2




                                                5
Solve graphically: (2.5) x ≥ (4) x




                                     6