• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

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

Extracts from this document...

Introduction

Population Trends In China

IB SL Mathematics Type II

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

Sean Okundaye

11/2/2011


CONTENTS

Introduction- Page 3

Modelling the population of China- Page 3

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

Additional data- Page 9


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.

Year

1950

1955

1960

1965

1970

1975

1980

1985

1990

1995

Population in Millions

554.8

609.0

657.0

729.2

830.7

927.8

998.9

1070.0

1155.3

1220.5

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.

...read more.

Middle

5 - 0.0167831966x4 + 0.3982148012x3 - 3.8791438329x2 + 22.6459713893x + 554.4475579557

As you can see, I have

If I substitute the elapsed time into the above equation, I get the following values:

Years After 1950

0

5

10

15

20

25

30

35

40

45

Population in Millions (My Model)

554.4

610.9

653.0

732.1

832.0

924.5

999.8

1071.3

1154.4

1220.9

Population in Millions (Original)

554.8

609.0

657.0

729.2

830.7

927.8

998.9

1070.0

1155.3

1220.5

We can now see my model in comparison to the other model.

image06.png

As one can see, my model has proven to be very accurate to the original data given the very minimal difference seen in the data and the graph. Indeed it is not necessary to revise this model.

RESEARCHER’S MODEL FOR THE POPULATION OF CHINA

A researcher has suggested that the population, “P” at time “t” can be modelled by:  
image07.png

We need to use a Graphical Display Calculator (GDC) to work out K, L and M. Given the five year intervals of the data, one can make “t” the number of years after 1950 and we already know that “P” means population. Therefore we have to input this into our GDC:

x(t)

0

5

10

15

20

25

30

35

40

45

y(P)

554.8

609.0

657.0

729.2

830.7

927.8

998.9

1070.0

1155.3

1220.5

...read more.

Conclusion

Additional Data

Let’s now look at additional data on population trends in China from the 2008 World Economic Outlook in conjunction with my model and the researcher’s model.

Year

1983

1992

1997

2000

2003

2005

2008

Population in Millions (Original)

1030.1

1171.7

1236.3

1267.4

1292.3

1307.6

1327.7

Population in millions (My Model)

1030.1

1227.5

1171.7

1125.9

1125.9

1097.6

1125.9

Population in millions (Researcher’s Model)

1045.6

1173.6

1225.2

1256.8

1305.2

1326.4

1348.9

As one can see, the best model for the new data is the researcher’s model. However, I need to modify this model so that will best fit the data from 1950 to 2008.

I have found these knew values of K, L and M:

K= 1809.69011

L= 2.31173963

M= 0.03216208

With my revised model I have created this graph:

image09.png

As one can see, the modified model fits all the data relatively accurately, proving that the researcher’s model, when revised works best.

Throughout this project I have used Microsoft Excel and a GDC for my work.

 | Page

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Math IA -Modelling Population Growth in China.

    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.

  2. Math Investigation - Properties of Quartics

    - a2 = 0 We can find the roots of the function quadratic equation The ratio of PQ: QR: RS is therefore Divide by a to set QR equal to one: The ratio therefore is: If calculated, it simplifies to -0.62: 1: -0.62 and 1.62: 1: 1.62 6.

  1. Derivative of Sine Functions

    State for what values of b the conjecture holds. For all values of b the conjecture holds. Because b determines the period of sine,cosine function. No matter b is positive or negative; the curve will be horizontal stretched by a factor of When b=0, f(x)

  2. Investigating Sin Functions

    OR The graph will undergo a phase shift of (-C). Part 4 - Findings Part 4 calls for me to predict the shape and position of three equations * Y = 3sin 2(x+2) * Y = .5sin3(x+1) * Y = -sin .5 (x-1)

  1. Finding Functions to Model Population trends in China

    I use (1955, 609), (1985, 1070) and (1960, 657.5) to find the parameters. These sets are chosen because they are the multiples of 5 or even integers, which are easier to calculate. 609=(1955)2 a+1955b+c 657.5=(1960)2 a+1960b+c 1070=(1985)2 a+1985b+c It would be difficult to calculate if I use the method with linear function.

  2. Maths Portfolio - Population trends in China

    approach is more detailed instead of the much broader one of the previous model. Points Value of the table (a) Value of the logistic curve (b) Difference between the values (b-a) Systematic error percentage ((b-a)/b)*100 50 554.8 546.8 -8 -1.5 55 609.0 611.3 2.3 0.4 60 657.5 680.4 22.9 3.4

  1. Population trends in China

    This model was introduced in the first cell and dragged down so that all cells followed the same rule. Model 554.8 603.5889 656.6682 714.4153 777.2407 845.5909 919.9517 1000.852 1088.866 1184.621 Model =554.8*(1.017^B2) =554.8*(1.017^B3) =554.8*(1.017^B4) =554.8*(1.017^B5) =554.8*(1.017^B6) =554.8*(1.017^B7) =554.8*(1.017^B8) =554.8*(1.017^B9) =554.8*(1.017^B10)

  2. A logistic model

    1.6u ?5 2 un?1 ? (?1? 10 )(un ) ? 1.6un {3} 3. Using the model, determine the fish population over the next 20 years and show these values using a line graph One can determine the population of the first 20 years just by knowing that u1=1?104 u2=1.5?104 .

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work