This document investigates population trends in China from 1950 to 2008 using different mathematical functions. It finds that an exponential function initially fits the data from 1950 to 1995 well but does not capture the leveling off of population growth seen in later data. A logistic function proposed by a researcher fits the full data set best, accurately modeling the population as it increased rapidly then began stabilizing in more recent years. The best fitting model will help understand and predict China's future population challenges.

1. Yuta Yamamoto
IB Math Study, Period 3
November 17, 2010
IA: Population Trend in China
Aim: To investigate different functions that best model the population of china from
1950 to 1995.
Table 1, Population in China from 1950 to 1995
Year 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995
Population
(Million)
554.8 609 657.5 729.2 830.7 927.8 998.9 1070 1155.3 1220.5
Graph1: Population in China from 1950 to 1995
From the table and graph above, it shows population of China is incredibly
increasing as year goes. If the points in graph are connected, the line seems like a
linear function, but also exponential function. Population is usually defined by
exponential function, so next step will find out how well exponential function fits
the original data.
Because this investigation only research during 1950 to 1995, 1950 is set as a 0 in
the rest of investigation.

2. Exponential function calculation
𝑦 = 𝑎𝑏 𝑥
609 = 𝑎𝑏5
, 1070 = 𝑎𝑏35
𝑎 =
609
𝑏5
, 𝑎 =
1070
𝑏35
609
𝑏5
=
1070
𝑏35
𝑏 = √
1070
609
30
= 1.018964099
𝑎 =
609
𝑏5
, 𝑏 = 1.018964099
𝑎 = 554.3995619
Exponential function equation
𝑦 = 554 ∗ 1.019 𝑥
Graph 2: Comparison between exponential function and original data.
This graph shows exponential function fits well to the data given. Since it is a
population growth, it supposes to fit well.

3. Researcher’s equation
𝑃( 𝑡) =
𝐾
1+𝐿𝑒−𝑀𝑡 where K,L and M are Parameters.
By using the TI-84 Plus Calculator
START ⇒CALC ⇒Logistic ⇒ENTER
Then the value of L, M, K will be found
L= 2.62
M= 0.333
K= 1950
Then P(t) =
1946 .18
1+(2.62∗e−0.33t)
Graph 3: Researcher’s equation and original data
The graph above shows how well researcher’s equation fits the original data
because the line passes at least 4 points in that graph.

4. The Population Growth for China in the Future
The Graphs shown in above implies the serious problem in Chinese population in
the future. These graphs show that population in China is increasing year by year.
Nowadays, China has a number 1 population in the world, so if it is still increasing,
it cause population explosion and many people will have a hard time to live.
Here are additional data on Population trends in China from the 2008 World
Economic Outlook, published by the International Monetary Fund (IMF)
Table 2: Additional data on population in China
Year 1983 1992 1997 2000 2003 2005 2008
Population
(Million)
1030.1 1171.7 1236.3 1267.4 1292.3 1307.6 1327.7
Graph 4: Comparison between IMF data and exponential function
It does not fit well to the data given. The data is going to stop increasing, but line
shows it is still increasing year by year.

5. Graph 5: Comparison between IMF data and Researcher’s equation
It fits perfectly to the data because the line passes though all points.
Table 3: All data on population in China
Year 1950 1955 1960 1965 1970 1975 1980 1983 1985
Population
(Million)
554.8 609 657.5 729.2 830.7 927.8 998.9 1030.1 1070.0
1990 1992 1995 1997 2000 2003 2005 2008
1155.3 1171.7 1220.5 1236.3 1267.4 1292.3 1307.6 1327.7

6. Graph 6: Comparison between all data and researcher’s model.
Researcher’s model fits the all data of population in China very well because line
though all points except 2. At first, the graph is increasing more and more each year.
However, it seems like going to stop increasing.
“I, the undersigned, hereby declare that the following assignment is all my own work and that I
worked independently on it.”
“In this assignment, I used LoggerPro” to draw my graphs.”