###### Example4.3.10

The following data, given in both table and graphed form, gives the counts of invasive cancer diagnoses in Oregon over a period of time. (wonder.cdc.gov)

Year | Invasive Cancer Incidents |

1999 | 17,599 |

2000 | 17,446 |

2001 | 17,847 |

2002 | 17,887 |

2003 | 17,559 |

2004 | 18,499 |

2005 | 18,682 |

2006 | 19,112 |

2007 | 19,376 |

2008 | 20,370 |

2009 | 19,909 |

2010 | 19,727 |

2011 | 20,636 |

2012 | 20,035 |

2013 | 20,458 |

What is the **rate of change** in Oregon invasive cancer diagnoses between 2000 and 2010? The total (net) change in diagnoses over that timespan is

Since \(10\) years passed (which you can calculate as \(2010-2000\)), the rate of change is \(2281\) diagnoses per \(10\) years, or

\begin{equation*} \frac{2281\,\text{diagnoses}}{10\,\text{year}}=228.1\,\frac{\text{diagnoses}}{\text{year}}\text{.} \end{equation*}We read that last quantity as “\(228.1\) diagnoses per year”. This rate of change means that between the years \(2000\) and \(2010\text{,}\) there were \(228.1\) more diagnoses each year, on average. (Notice that there was no single year in that span when diagnoses increased by \(228.1\text{.}\))