Fish

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FISH PRODUCTION SL TYPE II
Aim: This task considers commercial fishing in a particular country in two different environments – the sea and fish farms (aquaculture). The data is taken from the UN Statistics Division Common Database. The following table gives the total mass of fish caught in the sea, in thousands of tonnes (1 tonne = 1000 kilograms). Year

1980
1981
1982
1983
1984
1985
1986
1987
1988
Total Mass
426.8
470.2
503.4
557.3
564.7
575.4
579.8
624.7
669.9
Year
1989
1990
1991
1992
1993
1994
1995
1996
1997
Total Mass
450.5
379.0
356.9
447.5
548.8
589.8
634.0
527.8
459.1
Year
1998
1999
2000
2001
2002
2003
2004
2005
2006
Total Mass
487.2
573.8
503.3
527.7
566.7
507.8
550.5
426.5
533.0
Define suitable variables and discuss any parameters/constraints. Using technology, plot the data points from the table on a graph. Comment on any apparent trends in your graph and suggest suitable models. Analytically develop a model that fits the data points. (You may find it useful to consider a combination of functions.) On a new set of axes, draw your model function and the original data points. Comment on any differences. Revise your model if necessary. The table below gives the total mass of fish, in thousands of tonnes, from fish farms. Year

1980
1981
1982
1983
1984
1985
1986
1987
1988
Total Mass
1.4
1.5
1.7
2.0
2.2
2.7
3.1
3.3
4.1
Year
1989
1990
1991
1992
1993
1994
1995
1996
1997
Total Mass
4.4
5.8
7.8
9.1
12.4
16.0
21.6
33.2
45.5
Year
1998
1999
2000
2001
2002
2003
2004
2005
2006
Total Mass
56.7
63.0
79.0
67.2
61.2
79.9
94.7
119.8
129.0
Plot the data points from this table on a graph, and discuss whether your analytical model for the original data fits the new data. Use technology to find a suitable model for the new data. On a new set of axes, draw both models. Discuss how trends in the first model could be explained by trends in the second model. By...
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