Modeling Population Growth

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 = a0 + 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
a0 is the population in the initial period
Geometric Sequence

an = a0∙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
a0 is the population in the initial period
Post 1: Initial Response

Suppose you are working as an IT consultant and are known to have keen mathematical skills in addressing real-world situations. You have recently been contacted by a city council to present a plan for a population growth/decline initiative. The council has in recent years experienced considerably unexpected changes in population due to obsolete models and no use of technology. This has left them scrambling to find remedies for the city (e.g., new roads if the population is growing, repurpose vacant lots if the population is declining).

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.

Draft a detailed response to the council to demonstrate what you propose for more effectively modeling and preparing for population changes in the future.