Friday, 24 February 2012

Modeling Assignment - Graphs

Modeling Assignment

Linear Data
  • y= ax + b
  • straight line
  • first-degree polynomial function
  • linear data example:
http://illuminations.nctm.org/lessons/9-12/explorelinear/ExpLin-AS-Bike.pdf
  • this linear data provides with infromation about the maximum height (in inches) a bike can jump with a certain weight (in pounds); the lighter the bike is the higher it will jump in the air
  • this linear data will result in a straight line going from quadrant 2 to quadrant 4 with a function of        y= -0.156x + 13.348 and correlation coefficient of 0.9912 which means this data fits really good in a linear equation
Quadratic Data
  • y= x^2
  • porabola
  • second-degree polynomial function
  • quadratic data example:
http://babek.info/libertybasicfiles/lbnews/nl126/parabolicnally.htm
  • table 1 provides data for measuring a toss of a ball into the air; the relationship between time (in seconds) and hight (in feet)
  • this quadratic data will result in a up-side down parobala with a function of y= ax^2 + bx + c            y= -16.0876x^2 + 44.9695x + 10.0112 and R^2 of 1.00 (calculator doesn't provide r)
Exponential Data
  • growth y= 2^x, decay y= (1/2)^x
  • base is a fixed number and power is a varible
  • exponential data example:
http://www.btaworks.com/2009/08/19/who-might-be-the-next-120000-vancouverites/
  • this exponential data provides with growth of Vancouver population
  • in this data growth is not consisted and may have few peaks but in general data is exponential
Logarithmic Data
  • y= logx
  • a reverse of exponents
  • logarithmic data example (figure 4):
http://pediatrics.aappublications.org/content/124/4/e729.full
  • this graph shows the relationship between the calculations of how much mL of blood is lost during certain diseases and the error of those calculation
  • function for a log is y= a+b lnx

Sinusoidal Data
  • y= sinx
  • sine wave
  • sinusoidal data example:
http://www.austincc.edu/pmwright/sinusoidal.htm
  • this table provides data with a predator-prey relationship focusing on owl population over 12 years
  • the function is y= a*sin (bx+c)+ d                                                                                                     y= 25.7513*sin (0.5247x+-0.01826)+ 50.5617
Exploring Further 
-quadratic data
-excel spreadsheet: (email)



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