Population Growth Of Switzerland Case Study
Rationale: This math exploration is about the investigation of the modeling of the population growth of Switzerland over a period of 114 years, from 1900-2014, calculating the growth rate and predicting the future population. I chose this topic as I live in Switzerland and wanted to find out how the country has developed over 114 years. It therefore is of relevance to me. We were discussing population growth trends in geography class and it interested me how different countries had different growth patterns. In general, I wanted to learn more about modeling a population growth so that in the future, I can apply my new learning to other countries and overall gain more knowledge in this field of mathematics.
Aim: The aim of this exploration …show more content…
The usage of them depends on each population growth of an individual country. The logistic growth model, the logarithmic model, the mechanistic population model and the exponential model are the most frequently occurring functions.
Importance of modeling population growth: Modeling population growth is becoming increasingly important in today’s society, as more people are being born worldwide. Over the past few years there has been a boost in the amount of children being born. The increasing growth can have an effect on economy, education and the overall wellbeing of the people. The collected information can then be used by the government to meet the necessary needs, prepare and provide based on the current situation of the country, and if necessary, to take action if growth is going out of hand.
Malthusian Theory:
One of the first and most well known theories on population growth comes from Thomas Malthus, an English demographer (1766-1834) . He believed that earth could only provide for a specific population size, because food supplies are scarce. He thought that there was only a certain amount of land, so production of food could not increase with increasing population size. Malthus predicted that the population growth would one day outpace the food supply. His theory states that the population grows in a geometric progression, whereas the food has an arithmetic …show more content…
It determines whether an exponential growth or decay takes place. P(t) represents the value of the population. This is measured in at a yearly rate, as the different time values have a 1-year difference. This differential equation represents the difference rate of increase of population by the difference of the given time t. This equals the population at that growth rate r. It is the exponential population growth of Switzerland at a given time t. A is the initial population size, more exactly the size of the population at time 1900 and therefore the starting point. Variable t is the time period, which is 1 year.
Solving the differential equation:
1&2. Divide the left side by P(t)
3. The lift side of equation 2 can be written as a derivative of a differential equation.
4. r can also be written as a derivative of a differential equation.
5. Set up new equation with differentials.
6&7. Perform the inverse of ln on both sides 8. Rewrite the constant e as A. 9. The differential equation has been derived.
The logistic
Aim: The aim of this exploration …show more content…
The usage of them depends on each population growth of an individual country. The logistic growth model, the logarithmic model, the mechanistic population model and the exponential model are the most frequently occurring functions.
Importance of modeling population growth: Modeling population growth is becoming increasingly important in today’s society, as more people are being born worldwide. Over the past few years there has been a boost in the amount of children being born. The increasing growth can have an effect on economy, education and the overall wellbeing of the people. The collected information can then be used by the government to meet the necessary needs, prepare and provide based on the current situation of the country, and if necessary, to take action if growth is going out of hand.
Malthusian Theory:
One of the first and most well known theories on population growth comes from Thomas Malthus, an English demographer (1766-1834) . He believed that earth could only provide for a specific population size, because food supplies are scarce. He thought that there was only a certain amount of land, so production of food could not increase with increasing population size. Malthus predicted that the population growth would one day outpace the food supply. His theory states that the population grows in a geometric progression, whereas the food has an arithmetic …show more content…
It determines whether an exponential growth or decay takes place. P(t) represents the value of the population. This is measured in at a yearly rate, as the different time values have a 1-year difference. This differential equation represents the difference rate of increase of population by the difference of the given time t. This equals the population at that growth rate r. It is the exponential population growth of Switzerland at a given time t. A is the initial population size, more exactly the size of the population at time 1900 and therefore the starting point. Variable t is the time period, which is 1 year.
Solving the differential equation:
1&2. Divide the left side by P(t)
3. The lift side of equation 2 can be written as a derivative of a differential equation.
4. r can also be written as a derivative of a differential equation.
5. Set up new equation with differentials.
6&7. Perform the inverse of ln on both sides 8. Rewrite the constant e as A. 9. The differential equation has been derived.
The logistic