###### 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)

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 \(228.1\text{.}\))