# 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.

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Introduction

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.

Middle

This curve is and there are two relevant numbers to what the investigation gives in terms of numbers, the in the equation is again the point at which the curve intersects the 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 . The amount of times the 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.

The equation for this curve is 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 , from the previous graph I learnt that the curve had to be shifted upwards and to do so the had to be increased.

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

Conclusion

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)

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

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