MATH9G

Math Department Course: Math MYP 4 Teacher: Faris Salah
Date: 23. 03.2023 Criterion C

Sami kassis 9D
Name of Student:
Introduction:
In this assignment I will do a mathematical model that reflects the population
growth in any country I choose.
Mathematical modelling is an attempt to study some part (or form) of the real-life
problem in mathematical terms. Conversion of physical situation into mathematics
with some suitable conditions. Mathematical modeling can used in population
studies to help us predict and understand population trends. The country which I
want to study is Jordan and I will apply the three models (linear modeling,
quadratic equation modeling, and Exponential equation molding
Data Collection:
Population in Jordan Between 1970-2020
Table. 1
POPULAYION OF JORDAN BETWEEN 1970-2020
Year Population in millions

1970 1,557,374
1975 1,886,636
1980 2,216,903
1985 2,751,492
1990 3,480,587
1995 4,458,195
2000 5,056,174
2005 5,678,534
2010 6,931,258
2015 9,494,246
2020 10,928,721
Population in Jordan Between 1970-2020
Table. 1 second version
Table (1) 2nd version

x: Years (y): Population in millions
1 1557374
2 1886636
3 2216903
4 2751492
5 3480587
6 4458195
7 5056174
8 5678534
9 6931258
10 9494246
11 10928721
Mathematical Modelling
Linear modeling (y= mx+b )
Table. 2
Table (2): Comparing actual and calculated population data
y: population linear model
calculated
x: (y): Population in y = 898726x - 443257 percentage
Years millions Error%
1 1557374 455469 0.007075
2 1886636 1354195 0.002822
3 2216903 2252921 0.000162
4 2751492 3151647 0.001454
5 3480587 4050373 0.001637
6 4458195 4949099 0.001101
7 5056174 5847825 0.001566
8 5678534 6746551 0.001881
9 6931258 7645277 0.00103
10 9494246 8544003 0.001001
11 10928721 9442729 0.00136
Graph. 1

12000000
10000000
Population in millioms
f(x) = 898726.463636364 x − 443256.963636363

8000000
6000000
4000000
2000000
0
0 2 4 6 8 10 12
Years
Quadratic equation modeling ( y= a x 2+ bx + c )

Table. 3

y: population Quadratic
model calculated
y = 58748x2 - 253089x +
x: (y): Population in 997679 percentage
Years millions Error%
1 1557374 455469 0.007075
2 1886636 1354195 0.002822
3 2216903 2252921 0.000162
4 2751492 3151647 0.001454
5 3480587 4050373 0.001637
6 4458195 4949099 0.001101
7 5056174 5847825 0.001566
8 5678534 6746551 0.001881
9 6931258 7645277 0.00103
10 9494246 8544003 0.001001
11 10928721 9442729 0.00136
Graph. 2
Quadratic equation modeling ( y= a x 2+ bx + c )

12000000
10000000 f(x) = 58747.955155139 x² − 253089.378910795 x + 997679.138461539
8000000
6000000
4000000
2000000
0
0 2 4 6 8 10 12 14 16
Years
Exponential equation modeling ( P= A e

kt
)
Table. 4

x: (y): Population in y: population Exponential percentage
Years millions model calculated Error%
1 438386 551166.4731 0.257262944
2 622010 686933.0897 0.10437628
3 847936 856142.5499 0.009678266
4 1093474 1067032.695 0.02418101
5 1557374 1329870.559 0.146081443
6 1886636 1657452.216 0.121477479
7 2216903 2065725.742 0.068192996
8 2751492 2574567.641 0.064301244
9 3480587 3208750.514 0.078100759
10 4458195 3999149.1 0.102966761
11 5056174 4984243.385 0.014226293
12 5678534 6211991.976 0.093942904
13 6931258 7742166.93 0.116993038
14 9494246 9649263.715 0.016327544
15 10928721 12026127.97 0.10041495
Graph.3
Exponential equation modeling ( P= A e
kt
)
12000000
f(x) = 442232.876908311 exp( 0.220226296639009 x )
10000000
8000000
6000000
4000000
2000000
0
0 2 4 6 8 10 12 14 16
Years
Conclusion:
In conclusion we have analyzed the population growth of Jordan for the last
fifty years using the three models mentioned above, the linear graph doesn’t
fit because of the high % of error, the exponential model has a minimum fit
as it has less % percentage error but the best one that fit is the exponential
model as it has less % error and the best fit line passes through all the points.
The social economical factors that affected population growth in Jordan

 Health care
 Living standards
 Decreased infant mortality rates
 Increase in education
Based on the percentage of error we can say that the exponential model is
the most accurate model that can be used to predict the population growth
for Jordan.
The population of the country after 20 years based on the three models are:
Linear modeling 117,375,60
Quadratic equation modeling 194,350,99
Exponential equation 361,646,316

modeling
To improve our analysis, we could have used more sophisticated models in

addition to the impact of other factors such as migration.
While doing the analysis for this assignment we used;

o critical thinking skills while analyzing the population for Jordan
o Communication skills by showing my results
o Technology skills to analyze the data through excel sheet
o Research skills while researching for the needed data for Jordan
population

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Math Department Course: Math MYP 4 Teacher: Faris Salah

Date: 23. 03.2023 Criterion C

Year Population in millions

Table (1) 2nd version

POPULAYION OF JORDAN BETWEEN 1970-2020

f(x) = 898726.463636364 x − 443256.963636363

Quadratic equation modeling ( y= a x 2+ bx + c )

Table (2): Comparing actual and calculated population data

POPULAYION OF JORDAN BETWEEN 1950-2020

10000000 f(x) = 58747.955155139 x² − 253089.378910795 x + 997679.138461539

Exponential equation modeling ( P= A e

Table (2): Comparing actual and calculated population data

The social economical factors that affected population growth in Jordan

Linear modeling 117,375,60

Quadratic equation modeling 194,350,99

Exponential equation 361,646,316

To improve our analysis, we could have used more sophisticated models in

While doing the analysis for this assignment we used;

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