Search online to find out how many people are living in Manhattan and how many people are living in New York City's other four boroughs $($cite your source$).$ Assume that each year about $5\%$ of Manhattan's population moved out of Manhattan and into one of the other boroughs. Also assume that $4\%$ 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$.$ Represent the above migration as a matrix multiplication. Compare your matrix with the matrix from part $1.$ What is the relation?

b$.$ Calculate the distribution of the New York City population in terms of Manhattan and outside of Manhattan in $2024,2025,2026,2027,2028,2029,2030,2031$ and $2032.$

Assume the same migration trend for each year.

c$.$ Predict the long term New York City population distribution. Will population distribution stable. If Manhattan's population capacity is three million, will the population of Manhattan reach capacity under this model? If so$,$ when?

d$.$ How does your answer for question $g$ from part I will help you to answer question $c$ of part II$.$

e$.$ 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. I have trouble readingthe work if you can make sure its clear will leave a thumbs up please and thank u