# IB SL 1 Portfolio: Type 2 (Investigation)

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```					IB Math SL 1 Portfolio: Type 2 (Modelling)                                              Name ___________________
Date Set: Thursday, Oct 7th, 2010             Date Due: Wednesday, Oct 20th at 8:30am in the HS Office, and on turnitin.com

POPULATION TRENDS IN CHINA                                                                                      SL TYPE II
Aim: In this task, you will investigate different functions that best model the population of China from 1950 to 1995.

The following table1 shows the population of China from 1950 to 1995.
Year        1950     1955       1960      1965       1970      1975              1980      1985       1990      1995
Population    554.8    609.0          657.5       729.2      830.7       927.8   998.9     1070.0     1155.3    1220.5
in Millions
Use technology to plot the data points from the above table on a graph. Define all relevant variables and constraints clearly.

Comment on any apparent trends shown in the graph. What types of functions could model the behaviour of the graph?
Clearly define the parameters of your chosen functions. Explain your choices of functions.

Analytically develop one model function that fits the data points on your graph.

On a new set of axes, plot your model and the original data. Comment on how well your model fits the original data.

A researcher suggests that the population, P at time t can be modelled by

K
P (t)             M t
, where K, L and M are parameters.
1  Le

Use technology to estimate and interpret K, L and M. Construct the researcher’s model using your estimates.

On a new set of axes, plot the researcher’s model, your first analytic function and the original data.
Comment on how well the researcher’s model fits the original data. Comment on any differences between the two models.

Discuss the implications of each of these models in terms of population growth for China in the future.

Here are additional data on population trends in China from the 2008 World Economic Outlook, published by the International
Monetary Fund (IMF).
Year           1983           1992            1997           2000         2003          2005           2008
Population      1030.1              1171.7          1236.3           1267.4      1292.3           1307.6       1327.7
in Millions

Comment on how well each of the models above fit the IMF data for the years 1983–2008.

Modify the model that best fits the IMF data, so that it applies to all the given data from 1950 to 2008.

Comment on how well your modified model fits all the data.

___________________________________________________________________________________________________________________________
1
Data from the “land use change and agriculture program”, published by the International Institute for Applied Systems Analysis

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