# IB Math SL Portfolio Type 2 Population in China

by ishaan463 (student)

IB Mathematics SL

Math Portfolio

(Type 2)

Population Trends in China

Candidate Name: Ishaan Khanna

Candidate Session Number: 002603-011

Session: May 2012

The Doon School

Index

## Introduction

The aim in this portfolio is to study the different functions that best model the Chinese population from 1950 to 1995.

The following table shows the population of China between 1950 and 1995:

## Variables

The significant variables in this analysis are ‘x’ and ‘y’. The variable ‘x’ is for the different years from 1950 to 1995 with 1950 as 0. The population in millions is represented by the variable ‘y’.

## Parameters

The variables are time and population. Time (represented by x) cannot be negative and cannot decrease because it represents a unit of time. It can however increase infinitely. The variable population (represented by y) cannot be negative as population cannot go below 0. In this case the population also cannot increase infinitely as China will not be able to handle so many people. (Maximum carrying capacity of a country)

I will now list the values of ‘x’ and ‘y’.

## Modelling the population of China

Using technology[1] I graphed the given data to analyse the shape of the trend, shown in Graph 1.

Looking at the graph one can see a gradual increase in population between the years 1950 to 1995 at intervals of five years. At first, it seems as if it following a linear trend as it represents the overall population increase. However, it is not an accurate depiction of the data given to us. Below I have used ...