Population trends. The aim of this investigation is to find out more about different functions that best model the population of China from 1950 to 1995.

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Population Trends in China

The aim of this investigation is to find out more about different functions that best model the population of China from 1950 to 1995.

The controlled variables would be the place where the population was measured (China) and the amount of years between each reading (5 years every time the population is given). The dependant variable is the population in China and the independent variable would be the year at which the population was recorded.

The parameters leading to the amount of Chinese people involve the family planning policy, this mean that from 1970 onwards, urban families would only be allowed to have one child. However the majority of the population would be exempt from the rule because they are either rural families, ethnic minorities or if either parent was a single child he or she would be allowed to have more than one child. Fertility rate in China was 5 babies per woman until 1970, the new laws were implemented and there was a sharp reduction to 3 babies per woman in 1980. In 2008 the fertility rate was less than 2. The implementation of the restrictions helped the Chinese government to reduce an estimate of 400 million births since the policy was implemented. After the policy was implemented people in China looked for ways to only give birth to boys because they would be able to sustain the family, on the other hand girls wouldn’t. This idealism affected the population trends, the ratio became for every 100 girls born 119 boys were born.

Birth rates in China are currently at 14 babies born for every 1000 and the death rates are currently at less than 21 babies dead for every 1000. These numbers have been improving year over year, this means that there is less infant mortality rate and births have decreased. Again, the major thing affecting these numbers is that the government has restricted the number of babies a family can have. Doing so has made the health care system be more effective which leads to more prevention of diseases and death.

The investigation consists in finding a model that fits as close as possible the data given. This can be useful because the model can determinate how, if the parameters stay the same, the population numbers will be like in the future. However as parameters do change the models that are found will not be very precise to what the future could be, the past that is given can be modeled but that doesn’t mean it will be similar to it.

The data given shows, as a starting point the year 1950, it then continues for another 45 years of data which has been given in multiples of 5.

To make the investigation easier the data can be represented as  where  is the year given in the table. This will make it easier to manipulate the data and will give a graph starting at zero.

The graph for this data would be:

The graph above shows the trend that the population in China had, each of the axis is labled with it’s repsective meaning but they are actually represented on the model by having   for the years since 1950 and  for the population in millions.

The models I will be researching will be linear lines, polynomial (2nd and 3rd degrees) and exponential curves. I will also use trigonometry to find if a  or  graph can be similar to the data points. The least likely model to fit the data will be a logarithmic curve, however it will also be investigated.

I predict that a linear graph won’t suit the data points because the points are not linearly set. The  or  graphs might be able to represent the data points although further on in time the curve will drop meaning that the prediction is having a decrease in the population. A polynomial of 2nd degree will likely be similar in the way they behave as the trigonometric curves. They will drop down and in real life it wouldn’t apply because China’s population won’t decrease at the rate the graphs for a quadratic, or  would show. An exponential graph would only be able to represent the initial 20 years closely because further on it would increase at an even faster rate than that of the actual population.. The logarithmic curve isn’t likely to fit the data because it has a “L” like shape meaning that the initial years would be very far away from the model. The model I will develop will depend on how well it seems to fit into the data point set.

This model is , this is a linear equation, many points (represented by circles) are not close to the line and therefore the model is not likely to represent what happens next or what happened before because population doesn’t normally increase constantly, this is the case for population in China. The number which represents  is the only point which is exactly on the line, the year 1950 is represented as being the one on the  and at this point in time there was a population in China of 554.8 million people. This is actually the closest a linear equation can ever get to the data therefore it can’t be the model.

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The first trial at getting a model from a quadratic curve wasn’t at all successful. The current equation is , there are too many points of the data that means that there is no way that this can be the model, however the graph can still be manipulated to find a similar model. Again the  in the equation is relevant because it was the population at the year where the data given starts.

The curve for this model is represented by , it is the closest a quadratic curve can get before adding an  with 1 as its power. ...

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