• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5
  6. 6
  7. 7
  8. 8
  9. 9
  10. 10
  11. 11
  12. 12
  13. 13
  14. 14
  15. 15
  16. 16
  17. 17
  18. 18
  19. 19
  20. 20
  21. 21
  22. 22

Population trends. The aim of this investigation is to find out more about different functions that best model the population of China from 1950 to 1995.

Extracts from this document...


Population Trends in China

The aim of this investigation is to find out more about different functions that best model the population of China from 1950 to 1995.

The controlled variables would be the place where the population was measured (China) and the amount of years between each reading (5 years every time the population is given). The dependant variable is the population in China and the independent variable would be the year at which the population was recorded.

The parameters leading to the amount of Chinese people involve the family planning policy, this mean that from 1970 onwards, urban families would only be allowed to have one child. However the majority of the population would be exempt from the rule because they are either rural families, ethnic minorities or if either parent was a single child he or she would be allowed to have more than one child[1]. Fertility rate in China was 5 babies per woman until 1970, the new laws were implemented and there was a sharp reduction to 3 babies per woman in 1980. In 2008 the fertility rate was less than 2. The implementation of the restrictions helped the Chinese government to reduce an estimate of 400 million births since the policy was implemented. After the policy was implemented people in China looked for ways to only give birth to boys because they would be able to sustain the family, on the other hand girls wouldn’t. This idealism affected the population trends, the ratio became for every 100 girls born 119 boys were born.

Birth rates in China are currently at 14 babies born for every 1000 and the death rates are currently at less than 21 babies dead for every 1000. These numbers have been improving year over year, this means that there is less infant mortality rate and births have decreased.

...read more.


 curve and it doesn’t resemble the points at all, this will be changed as much as possible to find a way to make the curve fit the data points. The equation for the current graph is image60.png which allows for much manipulation. This is the model I am going to develop as it closely associates itself to the data, not when image13.png is multiplied by one but by less than one.image58.png

This curve is image62.png and there are two relevant numbers to what the investigation gives in terms of numbers, the image27.png in the equation is again the point at which the curve intersects the image31.png or the population axis. The number 665.7 comes from subtracting the population in the initial given year (1950) from the population in the final year, this is the amount of people which were born between those 45 years and to increase the amplitude of the wave it is put before image46.png. The amount of times the image13.png is multiplied changes the frequency and therefore a smaller frequency is needed. Currently it doesn’t look very much alike the data. The amplitude of the curve is too big and should become much smaller, this means that the change in population doesn’t really have an effect on the function.image00.pngimage00.pngimage61.png


The equation for this curve is image64.png and the changes come from having very big amplitude and a lot of frequency. I halved both the factors that affect the amplitude and the frequency to 332.85 and 0.1 respectively.

The sine curve starts to assimilate the points but it requires to be shifted towards the data points. The current equation is image67.png, from the previous graph I learnt that the curve had to be shifted upwards and to do so the image27.png had to be increased.image00.pngimage00.pngimage66.pngimage65.png

The shift of the curve was caused by having an equation with the parameters image68.png

...read more.


I believe that the limitations that this investigation has are very limited to China, the policies in place in China to control population growth are very strict and because that doesn’t happen in other parts of the world a trend line similar to china’s (not in numbers but in shape) might be difficult to encounter. A prediction of China’s population in the future is more difficult to predict after the second set of data was revealed. I believe this because is the population were to keep growing at a certain rate then that would be what is expected from a normal country, China is definitely the exception and mainly because of the factors affecting population growth. This has happened because there was too may people and therefore an intervention must take place.

The Chinese government probably used a model of their own , they must have found out that if the growth of population went at the same rate as it was going at that time they wouldn’t be able to control and govern that many people. I believe that is why the trend has a sudden drop in the increase of the population, the year 1970 was when the policies started to come into effect and 10 years later the population growth decelerated which made the anomalous curve of population in China between all those years.

[1] Xiaofeng, Guan, “Most people free to have more child”, In Chinadaily.com, 07/11/07, <http://www2.chinadaily.com.cn/china/2007-07/11/content_5432238.htm> (Accessed 26/09/10)

...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. 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 4:LinReg(ax+b), press enter. Hit the 2nd key, then hit the 1 key.

  2. Math Investigation - Properties of Quartics

    a vertical line of a function with a constant slope of a line. As the triangles are similar it is obvious that the ratios of its sides would be proportional which means that their ratios of sides for all the triangles would be equal.

  1. Stellar Numbers. In this task geometric shapes which lead to special numbers ...

    37.5 54 Difference between Sequence and n2 1 2.5 4 5.5 7 8.5 10 Second difference This second difference tells me the value for 'b' which is equal to . To find the value of 'c' I will use the previous methods: Using n=2: n2 + n + c = 10 (2)2 + (2)

  2. Derivative of Sine Functions

    At every /4 unit is shown in the table below: X -2 - - - - - - - 0 2.00 1.41 0 -1.41 -2.00 -1.41 0 1.41 2 X 2 1.41 0 -1.41 -2.00 -1.41 0 1.41 2.00 The scatter plots of values in the table is sketched below: (joined by a smooth curve)

  1. Investigating Sin Functions

    Y = -1sin(X) Y = -2sin(x) Y = -3sin(x) As we can see from the graphs, as these Amplitude numbers decrease, the graph gets stretched more, which directly contradicts what we figured out above. How do I explain this? Well, first we should consider the definition of amplitude, which is the 1/2 distance between the local extrema (Maximum and Minimum).

  2. Finding Functions to Model Population trends in China

    However, the coordinates above show to contain curves, which linear function cannot do, as it did not go through all the points. Also, if it happens to be linear function, it would mean that China's population would grow infinitely at a constant speed.

  1. Mathematics Higher Level Internal Assessment Investigating the Sin Curve

    First of all we examine the equation and identify the different variables. In this equation and . This means that the amplitude of the graph would be , causing the original curve to be stretched inwards, whereas the period of the new curve would be .

  2. Maths Portfolio - Population trends in China

    The average systematic error percentage is 1.7 %. Now we take in account the formula that the researcher suggested which is: , where K, L and M are parameters. With the use of GeoGebra4 we found the approximate values for K, L and M that best fit this model.

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