China therefore is a good case study in population growth trends, its analysis and prediction. This paper concentrates on population trends in China between 1950 and 2008, and outlines various models that could be used to represent the data.
A variable can be defined as a quantity or attribute that changes according to different situations in a certain process. In our case, the time (t) in years is a variable because it moves from 1950 to 1995. The second variable is population (P) of the people of China in millions. A parameter is a constant that varies from one group of equations to another. The parameters are m, the gradient and c the y-intercept. The graph below shows the population trends in China between 1950 and 1995.
Trends Seen in the Graph
From the graph, it can be noted that population in China has been increasing over the years. Between 1950 and 1975, the population increases at an increasing rate whereas, between 1975 and 1995, it increases steadily. This difference could be attributed to the one child policy that was introduced by the Chinese government in 1978, to curb population increase. The points in the above graph assume a linear pattern and if a line of best fit is drawn, it has a gradient of approximately 15.49 (calculated using technology). This means that China’s population grows by about 15.49 million people each year. The increase in population has remained steady probably because, there has been a decrease in the infant mortality rate and national deaths due to improved healthcare. Another factor could be immigration by people from other countries. The correlation coefficient (R2) is 0.994, translating to a 99.4% fit, which is a good fit. Functions that could Model the Behaviour of the Graph Some of the functions that could possibly be used to model the behaviour of this graph are, exponential, linear, logarithmic and polynomial functions. Starting off with the exponential function, it takes the form, The growth rate of an exponential function is proportional to its value. For example, if the rate of population growth is proportional to its size, then the population after t years will be Fig 2: Graph showing an exponential model of China’s population. The correlation coefficient in the above graph is 0.990 which translates to a 99.0% fit of the data points to the curve. This is a relatively good fit. However, the data points for 1970 up to 1980 are overestimated while that of 1995 is underrated. A linear function is one that can be written in the form, where m is the gradient and c is the y-intercept. A linear function often implies uniformity. Fig 3: A graph showing a linear model of China’s population. The correlation coefficient (R2) is 0.994 translating to a 99.4% fit of the data points to the line. This is a much better fit than the exponential model. In this model, the points in 1960 and 1965 are underestimated while that of 1950 is overrated. A logarithmic function can be defined as the inverse of an exponential function. It can be expressed by the following identity, Fig 4: A graph showing logarithmic model of China’s population. The correlation coefficient of the above graph is 0.994 translating to a 99.4% fit. It is similar to the linear function fit, but also better than the exponential model fit. The above three models can be used because they all have a 99.0% and above fit, which is an excellent choice as we cannot have real data with a 100% fit. Developing a Model Function that Fits the Data In this case, I choose to use a polynomial function. A polynomial function can be defined as a mathematical function consisting of several terms added together. This includes a linear function, which is discussed above. A polynomial