You can generally model population growth as either linear by an arithmetic sequence, or exponential by a geometric sequence. These can be defined by one of the general forms:

Arithmetic Sequence

an $=$ a$0+$ d$$n where,

d is the common difference $($change per year for population increase or decrease$)$

n is a natural number indicating the years since the initial period

a$0$ is the population in the initial period

Geometric Sequence

an $=$ a$0$rn where,

r is the common ratio $($multiple for population increase or decrease per year$)$

n is a natural number indicating the years since the initial period

a$0$ is the population in the initial period.

You will spearhead this initiative, and you are charged with planning a mathematical model for future use and prioritizing the city council's use of technology. Your goal is to apply your knowledge of sequences and create an appropriate mathematical model for the city's population growth$/$decline$.$ You will also share the technological tools that can be used to employ this model well into the future in the form of a computer algorithm.

In planning for your goal, you will want to briefly describe the city population growth$/$decline scenario and identify what factors might contribute to the growth$/$decline$.$ This initial stage of planning is critical in creating an accurate mathematical model. You also want to present how your model can be codified as a computer algorithm so that the council's staff can use it in the future.

As of $2022,89\mathrm{.}6\%$ of Chicago, IL residents were US citizens, which is lower than the national average of $93\mathrm{.}5\%.$ In $2021,$ the percentage of US citizens in Chicago, IL was $89\mathrm{.}4\%,$ meaning that the rate of citizenship has been increasing. Chicago, IL is home to a population of $2\mathrm{.}72$M people.

Which formula would I used and how would I do the algorithm?