1. **State the problem:** We are given a set of data points with years and corresponding values: (2013, 208.75), (2012, 225.75), (2011, 132), (2010, 178), (2009, 150.5), (2008, 217), (2007, 185.25), (2006, 162.75), (2005, 219.5), (2004, 164.71), (2003, 232), (2002, 228), (2001, 254), (2000, 303.6). We want to identify the pattern the data follows. 2. **Approach:** To find a pattern, we can analyze the trend of values over years. Common patterns include linear, quadratic, exponential, or no clear pattern. 3. **Check for linear pattern:** A linear pattern means values change by approximately the same amount each year. Calculate differences between consecutive years: $$\Delta y = y_{n} - y_{n-1}$$ Calculate some differences: - 2013 to 2012: $225.75 - 208.75 = 17$ - 2012 to 2011: $132 - 225.75 = -93.75$ - 2011 to 2010: $178 - 132 = 46$ - 2010 to 2009: $150.5 - 178 = -27.5$ The differences vary widely, so no simple linear pattern. 4. **Check for other patterns:** The values fluctuate up and down without a clear increasing or decreasing trend. This suggests the data might be irregular or influenced by other factors. 5. **Conclusion:** The data does not follow a simple linear or smooth pattern. It appears to fluctuate irregularly over the years without a clear mathematical pattern such as linear or exponential. **Final answer:** The data shows irregular fluctuations over the years with no clear linear or exponential pattern.