Population trends in China

Authors Avatar

Claudia Nevado        003656-008

MATHS COURSEWORK

POPULATION TRENDS IN CHINA

Claudia Nevado

INDEX

1. Finding my own model(s)

2. Research model using my own method and find K, L and M

3. Input new data using previous model and research model.

  1. The aim in this coursework is to investigate the different functions that best model the population of China from 1950 to 1995.

The following table shows the population of China between these years:

The relevant variables in this investigation are the population in millions in different years. The parameter is the initial population growth.

The data points from the table above are shown in the graph below, using Microsoft Excel showing the population in China from 1950 to 1995 (presenting the years from 0 being 1950, to 45 being 1995):

What I can observe according to the graph beside is that as the years pass, the population of China (in millions) increases gradually.

The functions which could model the behaviour of the graph can be any of the following:

· y = mx+c

The graph appears linear therefore we could use the above model, however it is geometric, as it is a population, therefore one of the following three may be better:

· y = ar (n-1)

· y = p (1+r) n

· y = a℮ (kt)

These can be used as they include in the equation population factors, where the year can be included in them as well as interpreting the graph with them.

By using the model of y = ar (n-1) which could be used in other terms as: y = ar t (t for time) I may develop this model with my data.

Again, I am referring to the years in terms of being from year 0 to 45 instead of from 1950 to 1995.

When t=0 then r to the power of 0 will be 1, meaning a will equal 554.8

Join now!

If I place other numbers from the data I can identify a more accurate response from what the equation would be.

By placing 10 in t and 657.5 in y the calculations would be the following:

657.5 = 554.8*r 10

1.186 = r 10

R = 10√1.186

R = 1.017

 

MODEL: y = 554.8*1.017 t

I introduced the data given to me in excel in the following way:

I introduced this model to see how accurate it would be in reference to the original data.

This model was introduced in the first cell and dragged ...

This is a preview of the whole essay