# Maths Portfolio - Population trends in China

Mathematics Portfolio

Topic: Populations trend in China
Date: 28.02.2012

In this portfolio, we should investigate and use mathematical functions and equations that would portray the model in the best way.

The relevant variables in this investigation are the population in millions in different years. The parameter is the initial population growth.

I have plotted the points given in the table above in the graph shown below.

*the year points of the picture above are replaced from 1950 to 50, 1960 to 60, etc. [plotted with Microsoft Excel 2007]

We can clearly see from the graph above that the obvious trend occurring is the rise of the population over a period of time and we can see it is increasing gradually, so we could possibly present the model through a linear equation like: Y = aX + b where a are the variables whilst b are the parameters.

Now I will try to develop the model using a linear function.

In order to start, we will firstly need to find the slope. And to find the slope, we divide the difference between the y-values with the x-values.

After the slope, we find the y-intercept, y1.

After we find this formula, we plot it into the graph, and we get the line that approximates the original points we got from the data. Below is the graph:

*graph above shows the linear function we found, plotted with the actual points. [plotted with GeoGebra4]

We can clearly see that the approach we took is close, but not accurate enough because the line does not pass through all the points, but merely touches them.
So by using a linear function we can try and be accurate with the points but it is not reliable when it comes to plotting population growth [or decay] because at one point we can see that the values become negative which is inaccurate and impossible for a population statistics. The linear function does not give us very accurate results about the long run as well, and it is most suitable just for portraying present data, because with this trend, it will show that the population will grow continuously and constantly up to infinity.

This model does represent our data quite accurately but as I discussed above, its limitatiations keep it from being an appropriate model for population growth. The average systematic error percentage is 1.7 %.

Now we take in account the formula that the researcher suggested which is:

, where K, L and M are parameters.

With the use of GeoGebra4 we found the approximate values for K, L and M that best fit this model.

K=2255
L=14
M=0.03

*year is shown as 50 – 1950, 70 – 1970 etc, whilst 100 represents 2000. [plotted with GeoGebra4]

We can clearly see that this ...