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

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[A] = [B] = [C] =

We can divide [A] from one side of the equation to isolate [C] so, [A]-1*[B]=[C]. We multiply by the inverse of [A]. Multiplying [A]-1*[B] we get the [C] to equal .

Graphing this we get the graph displayed below which we see looks identical to the original to the point where we do not even see the original graph.

Now we run the second function test to see how that one also fits the new data.

Again we have the equation P (t)=

Using a calculator we can run a logistical test on the original data where we get K to equal 1436, L to equal 1.36, and M to equal .0633. We get the data table below.

Year | 1983 | 1992 | 1997 | 2000 | 2003 | 2005 | 2008 | New Population in Millions | 1030.1 | 1171.7 | 1236.3 | 1267.4 | 1292.3 | 1307.6 | 1327.7 |

We then take this found data and see how well it fits the original data that we graphed earlier.

As we see the logistic equation fits the original data perfectly. Now let us see how both graphs look together when consolidated into one graph.

As we see here, the data from both the original graphs and their logistic functions line up quite well almost creating one continuous line. The models fit each other with no outliers and creating one solid line on the graph. The same can be seen with the second graph of the original data and the original IMF data and their respective polynomial functions.

In conclusion to this

We can divide [A] from one side of the equation to isolate [C] so, [A]-1*[B]=[C]. We multiply by the inverse of [A]. Multiplying [A]-1*[B] we get the [C] to equal .

Graphing this we get the graph displayed below which we see looks identical to the original to the point where we do not even see the original graph.

Now we run the second function test to see how that one also fits the new data.

Again we have the equation P (t)=

Using a calculator we can run a logistical test on the original data where we get K to equal 1436, L to equal 1.36, and M to equal .0633. We get the data table below.

Year | 1983 | 1992 | 1997 | 2000 | 2003 | 2005 | 2008 | New Population in Millions | 1030.1 | 1171.7 | 1236.3 | 1267.4 | 1292.3 | 1307.6 | 1327.7 |

We then take this found data and see how well it fits the original data that we graphed earlier.

As we see the logistic equation fits the original data perfectly. Now let us see how both graphs look together when consolidated into one graph.

As we see here, the data from both the original graphs and their logistic functions line up quite well almost creating one continuous line. The models fit each other with no outliers and creating one solid line on the graph. The same can be seen with the second graph of the original data and the original IMF data and their respective polynomial functions.

In conclusion to this