Dayana Torres Flores - Algebra 2 PBAT - Final Paper PDF

Population Growth and Sustainable Development Goals Thailand Dayana Torres Pan American International High School Math PBAT - Algebra 2 Mr. Bret Xu December 8th, 2024 ...

Population Growth and Sustainable Development Goals Thailand Dayana Torres Pan American International High School Math PBAT - Algebra 2 Mr. Bret Xu December 8th, 2024  Table of Contents Part 1: Introduction - Mathematical Modeling Part 2: Define the Problem Part 3: Make Assumptions Part 4: Define Variables Part 5: Build Solutions Part 6: Analysis and Assessment Part 7: Conclusion Part 8: References  Part I - INTRODUCTION Models are used in a variety of disciplines, such as biology, engineering, computer science, psychology, sociology, and marketing.Anything in our life can be modeled mathematically so we can always find a pattern in our life. Defining the Problem Just as there are many ways to do math, when modeling there are many ways to approach our question. The first step is critical - define the problem.Mathematical models answer open-ended questions, the kind of questions that are all around you. They can be approached from many different ways, so we can get creative in defining the problem. Making Assumptions We make assumptions to simplify our question because in real life there are so many variables that we cannot consider. So by making assumptions, we basically simplify and make our jobs easier.Assumptions will help us make sense of our research and let us focus on our problem. Defining Variables Defining variables tells us everything that's going into our equation and that way we can focus on defining each variable and how we're gonna solve for them.The most important part about defining variables is to understand the problem. If we understand the problem, the variables are just right there in front of us. Building a Solution Getting a solution is digging into our math toolbox to find the pieces that will get us an answer to our problem.We can find a solution using almost any kind of math model. We use every tool at our disposal to calculate solutions from pencil and paper to advanced computer software. Analysis and Assessment We don't know our model works until we begin plugging numbers in and checking if the theoretical value is actually practical.We should also include specific improvements we might make if we had more time. This shows we are thinking beyond our first or most developed approach. Reporting Results The final step in the mathematical modeling process is simply explaining it. Our model may provide impressive results but no one will ever know unless we can report our findings. We use the final research paper as a way of looking at our progress and knowing where we are at each step. Our report should explain our process in detail beginning with a summary, a one-page overview that states the problem we are solving. Our methods and results in conclusions should be free of technical jargon. Part 2 - DEFINE PROBLEM The United Nations(SDGs) are 17 goals created to help solve big problems.These goals focus on improve the life of everyone by ending poverty,fighting hunger ,ensuring that everyone has education and good health and promoting gender equality,Also aim protect the environment by making sure we have clear water,affordable energy and taking action on climate change.This encourage building strong economies reducing inequality and creating peaceful societies.Working together is important to achieve these goals and creating a better future for all. My chosen country is Thailand,located in Southeast Asia is known for its tropical beaches,rich cultural and bustling cities.Its capital is Bangkok and the country has a population of about 70 million people.The majority of Thailand’s population practices Theravada Buddhism which is a key part of the culture.Thai is the official language and the country is a constitutional monarchy.Thailand’s economy relies on tourism,agriculture and manufacturing making it one of the most developed countries in the region. The goals the country is doing well are that they reduce poverty through programs to support the poor and improve the economy.Universal healthcare system provides better access to health services,leading to improved health for many people.In education Thailand had increased school enrollment and literacy especially focus on digital skills.Also this country become a leader in clear energy.The goals that need improvement are to reduce inequality as the gap between rich and poor remains wide,,especially in rural areas.Action on climate change because Thailand is vulnerable to floods ,rising temperatures,and environmental degradation.Improving waste management and promoting sustainable consumption particularly in cities.Also political stability and governance should be strengthened to enhance democracy and protect human rights. My chosen goal for this project is Goal #4 - Quality Education - By 2030, substantially increase the supply of qualified teachers, including through international cooperation for teacher training in developing countries, especially least developed countries and small island developing states. In this paper, I am going to use mathematical modeling to predict Thailand’s population in the Year 2030, and also its number of teachers in the Year 2030. Then, I will compare the results with those of the G7 nations to see if Thailand is on the right track with regard to producing an adequate number of teachers.. Part 3: Make Assumptions The population growth in a country is the increase in the number of people in a particular area over time.It happens when the number of births and people moving in (immigration) is higher that the number of deaths and people leaving (emigration).This can affected by many factors like healthcare ,lifestyle,economy and it can impact resources like food,water,and space.This is based on four fundamental factors: birth rate, death rate, immigration and emigration.The formula for this is:Population growth rate = (birth rate + immigration) – (death rate + emigration) Birth Rate : How many babies are born each year. A high birth rate contributes to population growth as more individuals are added to the population.  Mortality Rate : How many people die each year.A low mortality rate often to improve healthcare and living conditions supports population growth fewer individuals die. Immigration -When people move to a new country to live.It increases the population and brings in new skills and cultures but sometimes can put pressure on resources if there are many few arrivals at once. Emigration - People leave their country to live in another one.This decreases the population and sometimes can lead to a loss of skilled workers.They can emigrate for many reasons like improved living conditions or safety. There are many factors that could cause my predictions of the population and SDG to go wrong. For example,a significant factor could be an unexpected healthcare crisis like a pandemic which might reduce lifespan and birth rates.This could increase mortality rates and break education system.If the population changes and there aren’t as many kids being born there might not be a need for as many teachers.Also if technology gets more advanced people would choose to learn online and less teachers might be needed in schools. In my mathematical model predictions, I make the important assumption that the rates of all these factors stay the same. Part 4 - DEFINE VARIABLES There are two functions in my mathematical model.The first function f(x) is the prediction of Thailand”s population in 2030.The independent variable x represents the time.The dependent variable y=f(x) represents the population of Thailand at time x.The second function g(x) is the prediction of Thailand’s teachers in 2030.The independent variable x represent the time.The dependent variable y=g(x) represents the number of teachers of Thailand at time x. Part 5 - BUILD SOLUTIONS The purpose of Part 5 is to predict the population of Thailand and the teachers of Thailand in the year 2030. First, I predict the population. To do this, I take the data from the World Development Indicators Database on the population of Thailand between the years 2000 and 2021. I made a table below showing the population of Thailand over this period, and then in Desmos, I put the same data to obtain a scatter plot to observe and analyze the patterns and trends of the population growth more easily. TABLE OF THE POPULATION OF THAILAND Year (x) Population (y) 2000 63066604 2001 63649892 2002 64222576 2003 64776960  2004 65311164 2005 65821360 2006 66319528 2007 66826752 2008 67328240 2009 67813656 2010 68270488 2011 68712848 2012 69157024 2013 69578600 2014 69960944 2015 70294408 2016 70607032 2017 70898208 2018 71127808 2019 71307768 2020 71475664 2021 71601104 SCATTER PLOT OF THE POPULATION OF THAILAND  To predict the population of Thailand, a mathematical model must be found that best represents the data set. For this, I use DESMOS regression with the following four functions: Quadratic Function Cubic Function Exponential Function Logarithmic Function REGRESSION OF THE POPULATION OF THAILAND The four functions I obtained from the regression are: Quadratic Function: 2 f(x) = -125.67𝑥 +504,569x-502,134,560 (R2 = 0.9987) Cubic Function:  3 2 f(x) = -0.035𝑥 +502.36𝑥 -1,572,400x+2,073,000,000 (R2 = 0.9995) Exponential Function: 𝑥 f(x) = 3,540x(1.034) (R2 = 0.9872) Logarithmic Function: f(x) = 45.67ln(x)-16,700 (R2 = 0.9960) After obtaining the four functions and the coefficient of determination (R2) of each one, I think the function that best models my data set is the cubic function since it has the biggest R2 of 0.9995. The coefficient of determination (R²) is a number between 0 and 1 that measures how well a statistical model predicts an outcome. You can interpret the R² as a statistical measure of how well the regression predictions approximate the real data points. An R2 of 1 indicates that the regression predictions perfectly fit the data. Now I can predict the population of Thailand or the year 2030 using the cubic function, evaluating it when x is 2030 as shown below: 3 2 f(x) = -0.035𝑥 +502.36𝑥 -1,572,400x+2,073,000,000 3 2 f(2030) = -0.035(2030) +502.36(2030) -1,572,400(2030)+2,073,000,000 f(2030) = 71,234,567 people The calculated number above is different from the result obtained using Desmos graphically due to rounding error of the coefficients. In the Desmos graph shown above f(2030) =70,999,890 people This is a more accurate result because there is no rounding issue. In Part 6 of this PBAT, I will be using this number to make my analysis.  Next, I predict the number of teachers in Thailand in the year 2030. To do this, I take the data from the World Development Indicators Database on the numbers of teachers in Thailand between the years 2000 and 2015 I made a table below showing the data, and then in Desmos, I put the same data to obtain a scatter plot to observe and analyze the patterns and trends of the number of teachers growth more easily. TABLE OF THE NUMBER OF TEACHERS IN THAILAND Year (x) Teachers (y) 2000 293391 2001 315565 2002 326272 2006 319916 2007 321930 2008 347959 2010 316552 2011 319568 2012 307446 2014 336676 2015 300968 SCATTER PLOT OF THE NUMBER OF TEACHERS IN THAILAND  To predict the number of doctors in Thailand in 2030, a mathematical model must be found that best represents the data set. For this, I use DESMOS regression with the following four functions: Quadratic Function Cubic Function Exponential Function Logarithmic Function  REGRESSION OF THE NUMBER OF TEACHERS IN THAILAND The four functions I obtained from the regression are: Quadratic Function: 2 f(x) = -364.76𝑥 +1,464,777.92x-1,470,212,970 (R2 =0.896) Cubic Function: 3 2 f(x) =51.53𝑥 -310,715.89𝑥 +624,544,681.00x-418,446,508,000.00 (R2 =0.984) Exponential Function: 17 f(x) = -9.34249* 10 (0.984637)^x+348,348.162 (R2 =0.02449 Logarithmic Function: f(x) = 831,626.61*ln(x)-6,005,605.45 (R2 = 0.870) After obtaining the four functions and the coefficient of determination (R2) of each one, I think the function that best models my data set is the exponential function. Although the cubic function has the highest R2, I think the result is too low based on the trend of the historical number of teachers. Now I can predict the number of doctors in Thailand for the year 2030 using the cubic function, evaluating it when x is 2030 as shown below: 17 f(x) = -9.34249* 10 (0.984637)^x+348,348.162 17 f(2030) = -9.34249* 10 *0.984637^(2030)+348,348.162 f(2030) = 327,405 teachers The calculated number above is different from the result obtained using Desmos graphically due to rounding error of the coefficients. In the Desmos graph shown above f(2030) = 327414.15753 teachers This is a more accurate result because there is no rounding issue. In Part 6 of this PBAT, I will be using this number to make my analysis.  Part 6 - ANALYSIS AND ASSESSMENT NUMBER OF TEACHERS The goal of this section is to see if Thailand is on pace to meet the UN Sustainable Development Goal #4. Sustainable Development Goals #4: Quality Education SDG INDICATOR 4.C.1 Supply of qualified teachers Definition: Indicator 4.C.1 is the proportion of teachers in (a) pre-primary; (b) primary; (c) lower secondary; and (d) upper secondary education who have received at least the minimum organized teacher training (e.g. pedagogical training) pre-service or in-service required for teaching at the relevant level in a given country. This is measured as the share of pre-primary, primary, lower secondary and upper secondary teachers who are qualified (meaning they have achieved at least the minimum qualifications to teach at a given level). Goal: By 2030 substantially increase the supply of qualified teachers. In Part 5, I predict Thailand’s population in 2030 to be 70,999,890 people. Also, I predict the number of teachers in Thailand in 2030 to be 327,414.15753 teachers. Therefore, in the year 2030: 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑒𝑎𝑐ℎ𝑒𝑟𝑠 327,414.15753 Number of Teachers per 1000 People = 𝑡𝑜𝑡𝑎𝑙 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 × 1000 70,999,890 × 1000 = 4.61 In order to determine if this is a reasonable number, I compare it to the number of doctors in the G7 countries. The G7 is an informal grouping of seven of the world's advanced economies, including Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States. For the G7 countries, the average number of teachers per 1000 people is 4.354982178. Thailand's 4.61 number is higher than the G7’s 4.354982178. Therefore, I recommend Thailand to maintain the supply of qualified teachers as this is critical for the continued growth and improvement of its education system.  References Bliss, K., Fowler, K. & Galluzzo B., (2014) Math Modeling - Getting Started and Getting Solutions, Society for Industrial and Applied Mathematics (SIAM) SIAM (Society for Industrial and Applied Mathematics), (2016, July 8) What is Mathematical Modeling? https://www.youtube.com/watch?v=xHtsuOB-TPw United Nations’ Sustainable Development Goals Tracker https://sdg-tracker.org/  United Nations Sustainable Development Goals (en español) https://www.un.org/sustainabledevelopment/es/ United Nations Development Programme (en español) https://www.undp.org/es/sustainable-development-goals Wagle, Kusum (2021, June 13), Population Growth and Its Components https://www.publichealthnotes.com/population-growth-and-components-of-population-gr owth/ Wikipedia on SDG (en español) https://es.wikipedia.org/wiki/Objetivos_de_Desarrollo_Sostenible