China Population Trends Practice Math Ia
Population Trends in China
The goal of this mathematical study is to explore the different functions that best model the population of China from the years 1950 to 1995.
Year | 1950 | 1955 | 1960 | 1965 | 1970 | 1975 | 1980 | 1985 | 1990 | 1995 | Population in Millions | 554.8 | 609.0 | 657.5 | 729.2 | 830.7 | 927.8 | 998.9 | 1070.0 | 1155.3 | 1220.5 |
Using the Chinese population data from 1950 to 1995, let us construct a graph using technology. Before graphing the data though, we must first determine the relevant variables, which are, the year and the population (in millions) of each coinciding year. The parameters are strictly confined to the data for the years 1950 and 1995 in the sense that the data cannot fall below the population number for the year 1950 and cannot fall above the data for the year 1995.
Upon reviewing the graph, we notice that the data appears to increase, but not precisely in a straight line. Going through the trend lines on excel, we find that the trend line that fits the best is the polynomial trend line, which is displayed in the graph down below. If we were to analytically develop one model function to determine if the polynomial trend line is indeed the most accurate fit, I would propose creating a system of equations.
Before jumping to far ahead, we need to make it clear the equation we are going to be analyzing. We will use the equation given to us by the polynomial trend line which is: y= ax2 + bx +c and the reason that we are using this equation is because of the fact that the R2 value is 0.9955. The closer the R2 value is to 1 the better it will fit the graph.
We will rearrange the equation y= ax2 + bx +c so that we can solve for the unknowns which are, the letters a, b and c. To do this, we need to add data to the equation and create three matrices. In order to continue on, let us first add the known values to the equation.
Given y= ax2 + bx +c , we know that the y-values are China’s population
The goal of this mathematical study is to explore the different functions that best model the population of China from the years 1950 to 1995.
Year | 1950 | 1955 | 1960 | 1965 | 1970 | 1975 | 1980 | 1985 | 1990 | 1995 | Population in Millions | 554.8 | 609.0 | 657.5 | 729.2 | 830.7 | 927.8 | 998.9 | 1070.0 | 1155.3 | 1220.5 |
Using the Chinese population data from 1950 to 1995, let us construct a graph using technology. Before graphing the data though, we must first determine the relevant variables, which are, the year and the population (in millions) of each coinciding year. The parameters are strictly confined to the data for the years 1950 and 1995 in the sense that the data cannot fall below the population number for the year 1950 and cannot fall above the data for the year 1995.
Upon reviewing the graph, we notice that the data appears to increase, but not precisely in a straight line. Going through the trend lines on excel, we find that the trend line that fits the best is the polynomial trend line, which is displayed in the graph down below. If we were to analytically develop one model function to determine if the polynomial trend line is indeed the most accurate fit, I would propose creating a system of equations.
Before jumping to far ahead, we need to make it clear the equation we are going to be analyzing. We will use the equation given to us by the polynomial trend line which is: y= ax2 + bx +c and the reason that we are using this equation is because of the fact that the R2 value is 0.9955. The closer the R2 value is to 1 the better it will fit the graph.
We will rearrange the equation y= ax2 + bx +c so that we can solve for the unknowns which are, the letters a, b and c. To do this, we need to add data to the equation and create three matrices. In order to continue on, let us first add the known values to the equation.
Given y= ax2 + bx +c , we know that the y-values are China’s population