Example 4.3.10

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

\begin{equation*} 19727-17446=2281\text{.} \end{equation*}

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 \(228.1\text{.}\))

in-context