Math Homework Help

The Solar Cycle

Directions: You may work individually, or in a group of size up to four people. If you work in a group turn in one project for the whole group. Identify all variables, include units when appropriate. Use complete sentences and explain your reasoning. If your best fit curve in question 4 is not correct the project will be returned to you and will not be graded until that portion of the project is done correctly.

Part I – The Solar Cycle

Sunspots are temporary visible spots on the surface of the sun. Sunspots have a periodic variation that has a period of about 11 years. To learn more about sunspots you can watch this NOVA documentary online. 

http://tinyurl.com/Math141SunspotVideo

In the table below is record of the average number of sunspots detected from 1965 to 2007

Source: Wikipedia

Year

Average number of sunspots

Year

Average number of sunspots

Year

Average number of sunspots

Year

Average number of sunspots

Year

Average number of sunspots

1965

15.1

1975

15.5

1985

18

1995

17.5

2005

29.8

1966

47

1976

12.6

1986

13.4

1996

8.6

2006

15.2

1967

93.8

1977

27.5

1987

29.4

1997

21.5

2007

7.5

1968

105.9

1978

92.5

1988

100.2

1998

64.3

1969

105.5

1979

155.4

1989

157.6

1999

93.3

1970

104.5

1980

154.6

1990

142.6

2000

119.6

1971

66.6

1981

140.5

1991

145.7

2001

111

1972

68.9

1982

115.9

1992

94.3

2002

104

1973

38

1983

66.8

1993

54.6

2003

63.7

1974

34.5

1984

45.7

1994

29.9

2004

40.4

Table 1 – Source: wolframalpha.com

1) Create a scatterplot for the sunspot data, include a proper title for your graph and label both your axes. Copy and paste your scatterplot into the space below. Do not include a trendline in this scatterplot.

2) From the scatterplot in part 1) estimate all the years in which there was a minimum of solar activity.

3) From the scatterplot in part 1) estimate all the years in which there was a maximum of solar activity.

4) Create a scatterplot with a best fit curve for the sunspot data. Estimate values for A, B, C, and D and then use the ‘Calculate Regression’ tool to find the Best curve. Include a proper title and label your axes. Copy and paste below.

5) Write down the equation for the best fit curve. Identify variables used, include units, round values to the nearest hundredth.

6) Using the best fit curve what is the average number of sunspots?

7) What does the model predict the period of sunspot activity is? Round your answer to the nearest hundredth.

8) Solar scientists have numbered each solar cycle. For example the solar cycle that began in about 1975 is solar cycle 21. The one that began in about 1986 is solar cycle 22. We are presently in solar cycle 24 which began in 2008. According to your model in what year will solar activity reach a maximum?

9) Use your model to predict the number of sunspots in that year.

10) Solar cycle 24 has been described as “the weakest in 100 years.” and “off to a sputtering start”. Use the data in the table below to explain why solar cycle 24 is described in this way. 

Hint: You might want to use your model from earlier to predict the average number of sunspots for each year listed below.

You can read more about this by reading the following article.

http://tinyurl.com/Math141SunspotArticle

Year

Average number of

sunspots

2008

2.9

2009

3.1

2010

16.5

2011

55.7

2012

57.7

2013

65

2014

79

Table 2 – Source:  wolframalpha.com