###### 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

\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