Text: Linear Algebra
In 2018, there are an estimated 1.632 million people living in Manhattan and a total of about 8.4 million people living in New York City's five boroughs. Assume that each year about 4% of Manhattan's population moved out of Manhattan and into one of the other boroughs. Also assume that 3% of the population of New York City's four outer boroughs moved into Manhattan each year. For simplicity, also assume that there were no other migrations and that there is no population growth.
a. Calculate the distribution of the New York City population in terms of Manhattan and outside of Manhattan in 2019, 2020, 2021, 2022, 2023, and 2024. Assume the same migration trend for each year.
b. Predict the long-term New York City population distribution. If Manhattan's population capacity is three million, will the population of Manhattan reach capacity under this model? If so, when?
c. The above mathematical model is oversimplified. If you want to incorporate the growth rate or immigration from outside of New York City, describe how you could make the model more realistic. Please be specific.