China is the latest entrant in the league of big world giants and superpowers. Although very rich in culture and history and having provided a self sustained backgrounds for more than 4 millennium this past century saw China experience continuous war, revolution and starvation, dominance, drug and opium addiction amongst the masses. These experiences made the Republic of China go through a phase of turbulence, chaos and economic weakness. But one thing which was evident was the fact that even before 1950; China had demographic features of a pre-modern society with increased mortality and fertility rate.

Following the foundation of "The People's Republic of China" in 1949, peace was restored and China began its demographic transition with a lot of controls under the new and visionary leaderships. The mortality rate dropped spontaneously and the fertility rate was recorded at about an average of six children per woman for a certain duration which is one of the all time highs for the entire world. Due to this, China began to grow rapidly. In this paper vide various means it will be checked as to which functions set the best model the population of from 1950 to 1995.

As shown in the graph above, the population census are given in interval of five years from 1950, and it span up to 1995. According to the graph, the population appears to increase gradually since 1950 by an average of 50-80 mn every 5 years. The behavior of graph could best be modeled by linear function, because this graph can yield a straight line. According to the book titled *The Theory of Functions of a Real Variable and the Theory of Fourier's Series*, linear function in the two intervals which are relative to one another at isolated point must be identical (p. 281). The population record can be the x variable which changes (increase), with times. For instance in our case, the population increase as years progress. The model function can be; p = mx+c which is a clear representation of any liner function / straight line. In this equation:

X is the variable time

P is the population

M is the pace / gradient at which population increases with passage of time

C is the constant that is implying the actual increase in population devoid of all other factors.

It is worth mentioning here that this is simplest and rawest form of an equation to assess and analyze a linear function / co-relation. But if the variables are correct the answers should be close to what is transpiring in actual.

Using the data that has been made available on a 5 yearly intervals we would be able to derive an equation which stands at:

Population = 1.84X + 5.4

The above graph shows how the original data can be demonstrated by the model function, which is the linear function. This graph clearly depicts the growth of population with the increment over the interval of 5 years. In accordance to the linear model, the population of China steadily increases with time and graphically can be represented with a straight line. Linear graphs cannot and should not be looked in isolation. Population booms are inversely linked with literacy rates, awareness, economic booms etc. On analyzing closely it is evident that right about the time China started warming up to Capitalism and saw an economic boom was the time when the actual increase in per capita population began to slow down. Thus the correlation in terms of market factors and economic forces and the overall population are pretty evident.

Another way of analyzing a linear function is by looking at a more detailed and comprehensive liner function such as:

P(t) = k/1+Le^{-mt } Where, K, L, and M are parameters / variables

As shown in the above equation, when value of K & L will be high population figure is bound to be higher and vice versa. On the other hand a higher value of M will result in a lower population and vice versa.

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The estimation model can be associated to the entire class of nonlinear appropriate extrapolation approach, categorized by the one-sequence estimation. The China population has been modeled using only one object's own sequence as per the set series. In this model relevant contributing factors with direct or indirect impact to the population growth, though not stipulated can be determined.

The population subject is determined by the quality of the population and demographic organization among other factors. A continual increment is directly associated to the China's social and economic maintainable advancement but this level has shown a trend of increase at a declining pace. With reference to matters pertaining to China's population, there has been a wide range of findings and accumulated data. Perceived from China's real situations and population growth, the mentioned feature, do establish a mathematical model or population increase in China.

Population size, eminence and age distribution has direct effects on a religion's fiscal advancement, resource share, social security, and urban strength. China has put in place plan of modernization, which aims at attaining economic growth, increased society resources, and improved environment. In order to effectively achieve these goals, government should be more comprehensive and have a systematic analysis of population concerning the population growth. In order to give the government its due credit it is evident that over the past 3 decades successive governments have assigned good importance to the authenticity of the consensus as well as to ensuring that population booms are controlled. Policies have been made and sent into mass circulation which makes it easier for the masses to follow the same.

The latest research on China population is recorded as follows from 2008 World Economic outlook published by the international Monetary Fund (IMF). These records can also be represented graphically as shown below;

Population in Million

According to this graphical representation if very clear that the China population growth is gradual from the year 1992 up to 2008. However, there is a notable growth which cannot be ignored. This change in population growth in the first study, which was for the period between 1950 and 1995, and the second one between 1893 and 2008, is attributed by the policies and measures which the Republic of China had put in place to curb the population growth among other factors, which might be contributing also. This population jump might seem large to many but then again this is the data of the world's largest country, around 17% of world's population, with a very high base even with a stagnant increment the portion of increase comes out to be in millions. This is a nation where even with such control each day 18 to 20 thousand babies are born on average.

Comparison of 1950s data to the IMF data pertaining to the period from 1990 onwards is not a realistic and pragmatic one because of the differential in market dynamics and change in market's approach as well as government's own approach. 1990s onwards has been the period of growth and development for China where nation's complete focus has been on the economy and output wherein population growth began to stagnate on its own.

However applying variables pertaining to each era and each factor has to be accounted for. That is why China's population trends and analysis can be figured vide multitude of ways and numerous variables and graphs can be plotted to give an insight on as to how this nation has grown and managed to stay afloat in such an organized manner. But the point would remain that one would be required to assess and check details not in isolation but in totality.