Final answer:
The subject of population dynamics in city migration problems involves applying mathematical models to demography, which is the study of population characteristics and dynamics. Variables such as birth and death rates are used to calculate population growth and predict future population sizes, considering factors like fertility, mortality, and urban migration.
Step-by-step explanation:
Studying population dynamics involves exploring how populations change over time due to births, deaths, and migration. The process can be quantified using mathematical models, with specific variables representing rates of births, deaths, and migration movements. In the context of city migration problems, as indicated in the student's question, the aim is to calculate the overall change in a population within a specified period. This is essential in demography, which is the scientific study of population characteristics and dynamics. For example, if a country has a population of 20 million and has a birth rate of 35 per 1,000 and a death rate of 15 per 1,000, it means that for every 1,000 people, there would be 35 births and 15 deaths in a year. This leads to a net population increase of 20 people per 1,000 per year. By applying this net increase across the entire population, one can ascertain the overall population growth rate and predict future population sizes. When considering the doubling time of a population, such as the example town starting at 100 people and doubling every 10 years, the use of exponential functions is essential in verifying the time it takes to reach a certain population size. Urbanization, detailed in Figure 19.3, discusses the migration from rural areas to urban centers, leading to rapid population growth in cities during the late 1800s. Alongside migration patterns, fertility, and mortality rates are central in understanding the changes in population size. This understanding is crucial, especially when considering the planet's exponential population increase, possibly reaching 8 billion within the current decade, as mentioned in the given context.