Essay
ACT B MAT135 Report
- Course
- MAT135
- Institution
- University Of Toronto (U Of T )
This is the 2nd math report in the MAT135 course. This is a good example to use as reference for ACT B.
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By: mplongo90 • 1 year ago
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ACT B: Population ForecastingI. Introduction
This model is intended for the Council of Denpasar, Bali, that may provide insight into future government
decisions on resource allocation. Denpasar serves as the industrial heart of Bali, and as a general hub for
tourists. With this in mind, the following population forecasts for years 2023, 2028, 2050 and 2100 will greatly
inform infrastructural policies.
i. Obtained Population Data
Table 1. Population of Denpasar from 1990-2021
Data retrieved from World Population Review, which uses data from the United Nations. This was the only source I found for Denpasar
which spanned 20+ years till 2021.
Year Population Growth Rate Growth
1990 206348 0.0464 9149
1991 223427 0.0828 17079
1992 246137 0.1016 22710
1993 271083 0.1014 24946
1994 298598 0.1015 27515
1995 328905 0.1015 30307
1996 362336 0.1016 33431
1997 399060 0.1014 36724
1998 439564 0.1015 40504
1999 484179 0.1015 44615
2000 533310 0.1015 49131
2001 554925 0.0405 21615
2002 577447 0.0406 22522
2003 600884 0.0406 23437
2004 625306 0.0406 24422
2005 650650 0.0405 25344
2006 677057 0.0406 26407
2007 704537 0.0406 27480
2008 733172 0.0406 28635
2009 762887 0.0405 29715
2010 791502 0.0375 28615
2011 809159 0.0223 17657
2012 827235 0.0223 18076
2013 845663 0.0223 18428
2014 864528 0.0223 18865
2015 883814 0.0223 19286
2016 903530 0.0223 19716
2017 923686 0.0223 20156
2018 944292 0.0223 20606
2019 965359 0.0223 21067
2020 986853 0.0223 21494
2021 1008709 0.0221 21856
Initial observations of the table reveal an increasing population with a decreasing growth rate.
, ii. Constraints and Shortcomings of Data & Model
The data doesn’t reveal any information on the 2020-2022 pandemic outflow. According to another source, the
population in late 2020 was “725,314” down from a high of “879,098” in 2015 (“Indonesia”). This is significant
when comparing my data showing Denpasar had 986,853 people in 2020. However, different sources identify
the Denpasar region differently, and would explain why my data (covering the entire Denpasar Metropolitan
Area) reveals larger figures.
Furthermore, in ACT A I provided the equation
𝑃 = 𝑅𝑁𝐼 + 𝑚𝑖𝑔𝑟𝑎𝑡𝑖𝑜𝑛 ,
However, I was unable to find this data, which would have permitted a model accounting for migration and the
impact and recovery of the pandemic.
II. Mathematical Model of Population Forecast
i. Exponential Model
Firstly, Table 1 has varying growth rates, so I’ll model future growth rates to forecast the population through a
composite function
𝑦 = 𝑃(𝑟(𝑥))
where 𝑃(𝑥) is the population and 𝑟(𝑥) is growth rate at 𝑥 years after 2021.
I modelled the growth rate to get 𝑟(𝑥):
Figure 1. Growth Rate of Denpasar, Bali 1990-2021
From the trendline,
−0.0617(𝑥)
𝑟(𝑥) = 0. 123𝑒 ,
where 𝑟(𝑥) is a function of growth rate, and 𝑥 is the number of years after 1990.
So the growth rate for 2021+ is given by:
−0.0617(𝑥+31)
𝑟(𝑥) = 0. 123𝑒
Example Calculation for 2023 Growth Rate
𝑥 = 2023 − 2021 = 2
−0.0617(2+31)
𝑟(2) = 0. 123𝑒
−0.0617(33)
= 0. 123𝑒
𝑟(2) = 0. 016056028
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