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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
(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
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