# An investigation of different functions that best model the population of China.

CONTENTS

Introduction- Page 3

Modelling the population of China- Page 3

Researcher’s model for the population of China- Page 8

INTRODUCTION

In this portfolio, I will be investigating a variety of functions in order to find out which ones best model the population of China from 1950 to 1955. In order to do this, I will be using a number of different technological methods which will help my investigation, with all my findings contained in this portfolio.

MODELLING THE POPULATION OF CHINA

The following table shows the population of China from 1950 to 1995.

As one can see from the data, there are two variables – the year and the population in millions. The year will be represented by x and the population will be represented by y There are restrictions that also need to be set; the year as well as the population can never be anything below 0. My parameter for time will be that for each year, “t” will equal the number of years after 1950. Therefore, for 1950, “t” will equal 0, for 1955 “t” will equal 5 and so on. Below is a graph that plots the above data points.

Looking at the graph, created using Microsoft Excel, one can see a gradual increase in population between the years 1950 to 1995 at intervals of five years. Below I have used several functions to decide which model will best fit the data.

Exponential

Logarithmic

Linear

Power of x

Polynomial (6th degree)

Indeed the rate of this increase constantly changes with it getting faster and slower. Therefore, it would not make sense to use an exponential, or indeed a linear model to best fit the data. An exponential model would ...