# Finding Functions to Model Population trends in China

Math Portfolio II

By Amber Perng

Aim: In this task, you will investigate different functions that best functions that best model the population of China from 1950 to 1995.

By plotting the above data points in autograph, we get:

Graph 1: Population of China 1950~1995

Variable

x-axis: the time (t)

y-axis: the population of China (p)

The above graph is plotted according to the population of China from 1955 to 1995. The points show that the population has increased at a constant rate, but had increased a little more from 1765 to 1970 comparing to other years, before it returned back to the constant increase.

To create a model function to fit the behaviour of this graph, I will use linear,

quadratic and exponential  functions to find its best fit.

Linear Function: y=ax+b

First, I use two points of (1955, 609) and (1985, 1070) from the given data to find the parameters of the function.

I chose these two points because they are the only two combinations that are all integers, which will be easier to calculate.

609=1955a+b

1070=1985a+b

Finding value a and b by using simultaneous equation:

1070=1985a+b

609=1955a+b

________________________________

461=     30a

a = ≒15.37

b = 609-1955×15.37=29439.35

Which gives the equation of y=15.37x29439.35 as below:

Graph 2: Population of China 1950~1995 with linear function

It appears to be rather fit to the coordinates. However, the coordinates above show to contain curves, which linear function cannot do, as it did not go through all the points. Also, if it happens to be linear function, it would mean that China’s population would grow infinitely at a constant speed.

Therefore, I have the conclusion that linear function is not the model of the graph.