MM250M3 COMPETENCY ASSESSMENT WRITTEN ASSIGNMENT

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∙r n 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 You are assuming the role of an IT consultant that is 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 population is growing, repurpose vacant lots if population is declining). You will spear-head 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 modelling and preparing for population changes in the future. Include all of the following in your detailed response. 1) In at least one well-composed paragraph, 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 2) 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 3) Review your initial model for accuracy by calculating the future population estimates for two values of n ≥ 5 years. 4) In at least one well-composed paragraph, reflect on the accuracy of your output (the future population estimates) and discuss whether the mathematical model is appropriate for your scenario. What limitations, or problems, may there be in using this model to estimate population indefinitely? Are there any changes that you would suggest to your general formula for the population sequence to represent a potentially better long-term model for the scenario? You may consider the factors that were described in the initial planning phase or other biological limitations on growth/decline of populations.