Briefly describe the situation in which population growth/decline is being considered and modeled

Learning Goal: I’m working on a algebra discussion question and need an explanation and answer to help me learn.

An example of how the response should be laid out is provided in the attached documents.

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

a_n = 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

a_n = 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.

View Unit 5 Discussion Post 1 example.

Include all of the following in your response.

1. Provide a narrative introduction to the planning initiative, where you:
   • Briefly describe the situation in which population growth/decline is being considered and modeled
   • State whether you project the population growth/decline to be linear or geometric in nature
   • Identify at least three factors you believe might be contributing to the unexpected population growth/decline (i.e., birth, disease, innovations, trends, migration)
   • Discuss and prioritize which of these factors you believe has possibly had the greatest impact on the population growth/decline
   • Reflect on how that factor may relate to one of the inputs in the model

1. Present your proposed mathematical model for how the council estimates the future population each year, using either an arithmetic or a geometric sequence. Clearly state the following:
   • Initial population size, a₀
   • Your change variable, d or r
   • The general equation for your model with these two inputs substituted into the formula

1. Write an algorithm that will take as input the number of years (n) since the initial period, and that will output the population size for each year from now until the nth year. Your algorithm must use an iterative operation (such as a while or for-next loop).