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Math IA -Modelling Population Growth in China.

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Introduction

Math IA

Year                                        Population in Millions

1950                                                        554.8

1955                                                        609.0

1960                                                        657.5

1965                                                        729.2        

1970                                                        830.7

1975                                                        927.8

1980                                                        998.9

1985                                                        1070.0

1990                                                        1155.3

1995                                                        1220.5

image00.png

In this set of data, the x axis is the year that the population was measured. The Y axis is the population in millions of China.

In this set of data the population before the year 1950 is not listed so that does not mean that the data before 1950 does not exist it just means that for the purposes of this investigation they are irrelevant. The time period or range of the data is only from the years 1950 to 1995, this limits the amount of data points we have, and restricts the overall trend of the graph that we can see. Instead of seeing the data from year 0, we only see it from 1950 to 1995. When you view this

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Middle

image04.png

This is a graph with the data points on it as well as a linear function:

y = 15.496x - 29690.2501

The function of the parent linear function is

image05.png

If in the TI-84 calculator you do a linear regression. You first need to put all the data from the years 1950 to 1995 into L1 and the corresponding population data into L2.

After you have put the data in the L1 and L2 lists. After the data has been entered into the lists. Press the 2nd button then the Y= button. Scroll down so that the 1: is highlighted. Press enter. Scroll to where it says "ON" and hit enter. Scroll down and select the line graph from the list of possible graph types. Make sure that the field labeled X List : is filled out with L1. Make sure that the field labeled Y List: is filled out with L2, press enter.

Hit Zoom, scroll down to 0:ZoomFit press enter. This will format your window so that you can view the data on the graph.

This graph is a graph of the data from the table.

To perform a linear regression hit the STAT button, scroll over to the field labeled CALC. Scroll down to the field labeled 4:LinReg(ax+b), press enter. Hit the 2nd key, then hit the 1 key.

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Conclusion

If the population of China follows the logistic function then in a few years China and its people will reach their breaking point, and the environment will begin to reach the carrying capacity. Also because of the natural way that populations grow, the logistic equation makes more logical since than my original interpretations of Westchester. With the logistic function I am better able to predict the population of China for the rest of many years.

        Both the linear function and the logistic function fit the data points from the data collected and reported. The linear function fits really accurately and does a good job of predicting the future data.

        My formula with the linear equation still is probably the most valuable source in determining the population for China. The linear function has a straight line that is very close to the data points. Other functions are also good at describing where the data points lie, such as the logistic equation that the researchers suggested. I would not modify my original linear equation because it works to predict the population of china. My function was very good at being able to predict the population of China.

Tyler Loving

2/14/12

Math IA

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