Case
MAT135 ACT B REPORT
- Course
- MAT135 (MAT135)
- Institution
- University Of Toronto (U Of T )
U of T MAT135 ACT B report. A good reference to use for the second report of MAT135.
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ACT B - FINALINTRODUCTION
In recent years, the multicultural and diverse border city of Windsor, Ontario has seen an
increase in population (“Windsor, Canada Metro Area Population 1950-2023 | MacroTrends”).
With further exploration, a model can predict how factors such as immigration and emigration
can anticipate the growth of Windsor’s population in years to come (Math Modeling: Getting
Started and Getting Solutions, Bliss, Fowler, & Galluzzo, 2014).
FIGURE 1 - TOTAL NET MIGRATION IN ONTARIO FROM 1972-2022
(“Windsor-Essex County Migration | CREA Statistics”)
FIGURE 2 - POPULATION GROWTH IN WINDSOR, ON FROM 1950-2030 (UN population
projection included)
(“Windsor, Canada Metro Area Population 1950-2023 | MacroTrends”)
POPULATION MODEL
The model shown below is a linear model which predicts the population growth of Windsor,
Ontario, assuming that the “most influential” factor which affects the population is immigration.
, Seeing as Windsor’s population is growing at a constant rate, it is also under the assumption that
emigration is no longer a factor affecting Windsor's population. Another assumption that can be
made is that birth and immigration are equivalent as they both add individuals to the population,
while death and emigration are equivalent as they both include individuals which disappear from
the population (Frederickson, Population Ecology). With this assumption in mind, birth and
death can be excluded as factors affecting Windsor’s population growth.
P(t) = P0 + (I ∙ t)
Where:
P(t) is the total population at time t, in years from P0
P0 is the initial population
I is the annual increase in population due to immigration
t is the number of years from P0
According to previously recorded data on Windsor, Ontario’s population, the city has seen an
average annual increase of approximately 1,450 people per year, between the years 2002 and
2022 (“Windsor, Canada Metro Area Population 1950-2023 | MacroTrends”).
I = (Population in 2022 - Population in 2002) / (2022 - 2002)
= P(20) - P(0) / 2022 - 2002
= 340,000 - 311,
= 1,450
Using this data, the model can now be displayed with a value for P0 (initial population in 2002)
and I, i.e. without any unknown parameters, as:
P(t) = 311,000 + (1,450 ∙ t)
This model predicts that the population of Windsor, Ontario will demonstrate a constant linear
growth with an average of 1,450 new habitants each year, starting from the year 2002, with an
initial population of 311,000 people.
PAST POPULATION
To verify the validity of this model, we can check how the model prediction compares to past
population data of Windsor, Ontario.
Predicted population size in 2005:
P(t) = 311,000 + (1,450 ∙ t)
P(3) = 311,000 + (1,450 ∙ 3)
= 311,000 + (1,450 ∙ 3)
= 315,350
Windsor’s population size in 2005 was actually 321,000 (“Windsor, Canada Metro Area
Population 1950-2023 | MacroTrends”).
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