7점 May 2023 IB Math AI HL IA

본 문서는 May 2023에 작성하였던 IB Math AI HL Internal Assessment입니다. 최종점수 7점을 받았습니다. 저의 토픽은 “Projecting the 2070 population of South Korea using Calculus and Statistics” 이었습니다.

[본문내용]

1. Introduction

The aging and shrinking population in developed economies, especially in my home country, South Korea, has been numerously covered by the media in recent years. I found this concerning as an economics student because aging population is directly linked to the country’s economic output and the burden placed upon the working population. Amidst such, I read a terrifying article claiming that the Korean population would decrease by 20 million by 2070, which is around 40% of the current
population. I wanted to see if I can use my mathematical knowledge to either refute or corroborate this accusation. Hence, my aim is to “project the 2070 population of South Korea using calculus and statistics”.

The population data could be easily collected on Korean Statistical Information Service (KOSIS), which is the government-run national statistical database. This means that the data is as credible as could be, compared to other sources. It also offers the data over a long period of time, from 1960 to 2021, which is 62 years’ worth of data. In statistics, 30 is a large enough sample as a rule of thumb, thus I am satisfied with this dataset from KOSIS. My first approach towards modeling the Korean population using this data will mainly involve calculus. After some time researching on population projection methods, I learned that two models, exponential and logistic models, are the most commonly used.

I could understand under what assumptions these models were built and could follow the mathematical steps in building those models. Therefore, I decided to derive and utilize these models to project the 2070 population of Korea. The second approach is a statistical approach. Contrary to the more ‘top-down’ approach of modeling with the whole population data, I decided to take a ‘bottom-up’ approach as well, by examining possible factors that contribute to population changes. I will explain which factors I chose to examine and why in the relevant section later on, but I did consider many different factors, ranging from fertility rate and accessibility to healthcare to economic output. The selection of factors will mainly be based on data availability as well as the result of the chi-square test for independence between each factor and population change. Then, using the final factors that I choose, I will perform multiple linear regression that would best suit the population data retrospectively…

• 총 페이지수: 20 pages
• 과목명: Mathematics
• 주제: Projecting the 2070 population of South Korea using Calculus and Statistics
• The file is in PDF format.