# Define the variables and write a mathematical model for this data..?how can I write a mathematical model/equation for this population data? 2000 82,210,000 2001...

Define the variables and write a mathematical model for this data..?

how can I write a mathematical model/equation for this population data?

2000 |
82,210,000 |

2001 |
82,333,000 |

2002 |
82,508,000 |

2003 |
82,541,000 |

2004 |
82,516,250 |

2005 |
82,469,400 |

2006 |
82,376,451 |

2007 |
82,266,372 |

2008 |
82,110,097 |

2009 |
81,879,976 |

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### 1 Answer

From a quick look through the population data, you can easily see that the population increases from the year 2000 to 2003, but decreases steadily after that.

Since the decreasing population seems to be the major trend, you can put this data into a simple graph equation:

1. think about a graph that would clearly show the population change over time: time as the x-axis and population as the y-axis.

2. Choose two coordinate points that would show the decreasing trend: I will choose the points (2004, 82,516,250) and (2006, 82,376,451) for my example.

3. Find the slope: slope=change in y/change in x=-139799/2

which gives us a slope approximately equal to -69900.

4. Now we have to find the y-intercept given as b:y=-69900x+b; you can plug in any of the coordinate points above into the equation to find b. b is approximately equal to 2.226*10^8

5. This completes the equation: y=-69900x+2.226*10^8

Creating an equation from a set of data really is quite simple, if you just try to understand what kind of trend the data is showing. Then it's just a matter of setting the x, y-axis and determining the slope.