Chapter 6.FOM, Problem 8P

Sunspot Activity Sunspots are relatively “cool” regions on the sun that appear as dark spots when observed through special solar filters. The number of sunspots varies in an 11-year cycle. The table gives the average daily sunspot count for the years 1968-2012.

(a) Make a scatter plot of the data.

(b) Find a cosine curve that models the data (as in Example 1).

(c) Graph the function you found in part (b) together with the scatter plot.

(d) Use a graphing calculator to find the sine curve that best fits the data (as in Example 2). Compare to your answer in part (b).

Year	Sunspots	Year	Sunspots	Year	Sunspots	Year	Sunspots
1968	106	1980	154	1991	145	2002	104
1969	205	1981	104	1992	94	2003	63
1970	104	1982	115	1993	54	2004	40
1971	67	1983	66	1994	29	2005	30
1972	69	1984	45	1995	17	2006	15
1973	38	1985	17	1996	8	2007	7
1974	34	1986	13	1997	21	2008	3
1975	15	1987	29	1998	64	2009	3
1976	12	1988	100	1999	93	2010	16
1977	27	1989	157	2000	119	2011	56
1978	92	1990	142	2001	111	2012	58
1979	155

Source: Solar Influence Data Analysis Center, Belgium