King Fahd University of Petroleum & Minerals

Math 202 - (072)Text Book: Differential Equations

Population of Saudi ArabiaProblem 39 … Page 101

TEAM MEMBERS

• AbdulAziz Al-Zahrani ME

• Redha Al-Shmmry ME

• Ahmed Ateen ME

• Atif Al-Zahrani ME

• Ameen Bin-Obadi EE

• AbdulLatif Al-Mutairi ME

• Mohammad Al-Ghamdi ME

INTRODUCTION & EPILOGUE :

AbdulLatif Al-Mutairi

PHYSICAL EXPLANIATION :

Ahmed Ateen

THE PROBLEM EXPLANIATION :

Mohammad Al-Ghamdi

SOLVING THE PROBLEM :

Atif Al-Zahrani & Ameen Bin-Obadi

CREATION THE SLIDES :

Redha Al-Shmmry & AbdulAziz Al-Zahrani

THE QUESTION

dt

dD

dt

dB

dt

dP

p(t)dt

dD

p(t)

dt

dB

pkdt

dB1 pk

dt

dD2

21 kk 21 kk 21 kk

Population Model In one model of the changing population of a community, it is assumed that

Where and are the birth and death rates, respectively.

a) Solve for if and .

b) Analyze the cases , ,and .

c) Use the statistics of Saudi Arabia given in class and Matlab to plot P(t) from 1990 -2020 and predict the population of Saudi Arabia in 2020.

THE SOLUTIONa)

mt

c

tkkC

ep(t)mkk

)t-k e(kp(t) e

p(t) at t

eetP

c)tk(kp

dtkkp

dP

dtkkPdp

pkpkdt

dD

dt

dB

dt

dP

16700 if

1670016700

16700at which19900have weIf

)(

ln

)(

)(

21

21

)(

121

21

21

21

1

211

b)

negative. is m where,167000 if

ith time.constant w 16700 if

with timeincreasing iswhich e 16700 P(t)

positive is If

21

21

tm

21

mt

etpmkk

tpkk

m kk

582.0

56.0167002425000013

6040167002350000012

24250000 2003

23500000 2002at

thatknew weclassin shown statistics theFrom

13

12

avg

m

m

m

mep

.mep

tp

tp

tetp 582.016700

0 5 10 15 20 25 300

2000

4000

6000

8000

10000

12000

14000

16000

18000

21 kk

21 kk

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6x 10

6

10 11 12 13 14 15 16 17 18 19 200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2x 10

9

20 21 22 23 24 25 26 27 28 29 300

1

2

3

4

5

6

7x 10

11

c)

2020

at population is which 103899.61670030

16700

582.0

1130582.0

582.0

ep

etp

mt

avg

THANK YOU