• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10
  11. 11
    11
  12. 12
    12
  13. 13
    13
  14. 14
    14
  15. 15
    15
  16. 16
    16
  17. 17
    17

Math SL Fish Production IA

Extracts from this document...

Introduction

003717-011

Fish Production

I-Shou International School

Mathematics Standard Level Internal Assessment

Type 2

Candidate Name: Hung Li Chu

Candidate Number: 003717-011

Word Count: 2886

Date of Submission: 26th October 2012

The aim of this internal assessment is to consider commercial fishing in a particular country in two different environments- the sea and fish farms (aquaculture). The table of values below is taken from the UN Statistics Division Common Database.

Table 1: This shows the total mass of fish caught in the sea between 1980 and 2006 in thousands of tonnes.                                           (1 tonne = 1000 kilograms)

Year

1980

1981

1982

1983

1984

1985

1986

1987

1988

Total Mass (tonnes)

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 (tonnes)

450.5

370.0

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 (tonnes)

487.2

573.8

503.3

527.7

566.7

507.8

550.5

426.5

533.0

Graph 1: This shows the total mass of fish caught between the years 1980 and 2006.

image00.png

Based on the graph, the x-axis represent the years between 1980-2006. The y-axis represents the total mass of fish caught in tonnes per year. The graph illustrates that in some years the total mass of fish caught increases whereas in other years the total mass of fish caught decreases. For instance, from 1980 until 1988, the total mass increases every year (426.8-669.9 tonnes). Then the total mass decreases from 1989 to 450.5 tonnes until 1992 where it increases again.  

In order to develop a function model that fits the data points, the graph above will be split into 3 sections similar to how the table of values are split in table 1. The values for the years would have to be rearranged. This is done so that at 1980 x=0, and a y-intercept would occur. Therefore, at x=0, the y-intercept should be 426.8.

...read more.

Middle

Judging from the function-modelled graph, the model seems to fit quite well onto the graph because the line passes through most of the points. However, there are limitations to this graph because it cannot be used to predict the values for the next few years. As seen in the original graph, the total mass decreases right after the 8th year. The total mass might have been affected by environmental factors such as pollution, which would contribute to the decreasing population in the sea. This would have an impact on the fish caught in certain years because if there were less fish available, the amount caught would also decrease.

Graph 4: This shows a computer generated linear function and the function model.

image05.png

The linear function model is not as accurate as the quartic function model because it does not pass through as many points as opposed to the other one. From the graph, the linear model does not pass through the points between the years 3-6 whereas the quartic model is more consistent as it passes through most of the points throughout the graph. Nevertheless, the linear function model has an advantage because it could estimate the total mass in the upcoming years provided that the total mass each year does not decrease.

In order to model the next set of values in the 2nd section, another function model will need to be considered because as seen in the quartic model, the graph keeps increasing. On the other hand, the total mass of the original graph plummets after the 8th year.

...read more.

Conclusion

Conclusion:

        In conclusion, both models could be used to predict future trends in both types of fishing provided that there are not external factors that might influence the total mass caught. The quartic and the quintic model are fairly accurate in modelling the total mass of fish caught in the sea. Both of the models could be used to predict future trends theoretically. However, these models have limitations because they cannot predict the exact values since the number of fish available each year varies. There may be more fish available in the sea in some years whereas in other years, this may decrease because the fish might have died due to pollution or other forms of human activity. The computer generated cubic model is more suitable when used to predict possible future trends because it is more accurate in modelling the total mass of fish from the fish farms. Since the fish are bred in fish farms, it is possible for people to control the total mass that is caught thus, indicating that the model could predict future trends to a degree of accuracy. By looking at the table of values, the total mass increases continuously every year because it has a lower chance of being affected by environmental or external factors that may decrease the mass of fish produced. Humans can control the number of fish in fish farms; since the total mass increased every year except for 2001 and 2002, it can be assumed that there is a high demand for fish by consumers. The possible reason for the decrease in numbers during the years 2001 and 2002 are probably due to the lower demand by consumers or the errors made by the breeders that resulted in the death of the fish.      

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Maths IA Type 2 Modelling a Functional Building. The independent variable in ...

    : 1 The efficiency is seen to be the same as when the fa�ade was on the shorter side of the base. After determining the efficiency, we find the area of the cuboid floor once again. Table 7. Area of cuboid floor when the fa�ade switches sides Maximum height of roof (m)

  2. Math IA -Modelling Population Growth in China.

    This graph is a graph of the data from the table. To perform a linear regression hit the STAT button, scroll over to the field labeled CALC. Scroll down to the field labeled LOGISTIC, hit enter. You will come up with a screen that looks like this: Logistic y= c/(1+ae^(-bx))

  1. Math Studies I.A

    870250000 5856.8409 Somalia 600 48.84 29304 360000 2385.3456 Spain 34,600 79.78 2760388 1197160000 6364.8484 Sudan 2,200 49.11 108042 4840000 2411.7921 Swaziland 5,100 32.23 164373 26010000 1038.7729 Switzerland 40,900 80.62 3297358 1672810000 6499.5844 Taiwan 31,900 77.5 2472250 1017610000 6006.25 Tanzania 1,300 50.71 65923 1690000 2571.5041 Timor-leste 2,400 63.5 152400 5760000 4032.25

  2. Math IA - Logan's Logo

    3.15+-2.8=0.35. Now, having graphed onto the axes, I can visually determine the horizontal shift of my graph. By extending the data points I plotted to meet the center line of the curve, I was able to estimate how many units leftwards my graph had shifted.

  1. Math Studies - IA

    These two numbers can then be compared. Whenever the calculated value is below 1, US wins, and when it is above 1, Europe wins. A value of 1 represents a tie because for example a Ryder Cup final score of 14 - 14 is ()

  2. Math IA type 2. In this task I will be investigating Probabilities and investigating ...

    p would be the probability of success and q the probability of failure and they would be Therefore: Therefore a randomly selected point varies from the mean by 1.491points and the mean is 6.667. Thus normally Adam will win points which means that Adam makes between 5.176 to 8.158points and

  1. Math IA patterns within systems of linear equations

    General solution to 2 x 2 system following a GS Because we have assumed that the coefficients in the equations follow the pattern of a GS we can produce a general model: where a is the first term and r the common ratio.

  2. Gold Medal heights IB IA- score 15

    since it?s in centre of the values gives. 216 = 19.5sin [ (1960-c)] + 216.5 -0.5 = 19.5 sin [ (1960-c)] ?0.0256410256410 ? sin(?/48(1960-c)) ?0.0256438361401? (?/48(1960-c)) - sin inverse applied ?0.3918089550276?1960-c - note: calculator in radiant ?1960.391808955 ? -c c?1960.391808955 c?1960.4 - therefore c is approximately 1960 Model of the

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work