How did you make your system on linear equations? Where did you get the 100? 10? 400? 20? 5:47Expert AnswerStep1a)#17P(e) = azt + a,t + a.249 million in1990281million in2000309 millionin2010at t=o, PC+) = 249at t=lo, P(t) = 281at te 20, P(t) = 309249 = 0+o + 4.281=a2(100) +9,(10)+ 90309=0 (400)+a,(20)+9oa.- 24 9S1stem 아equations(0o aatlo9, +9,= 20400 92 +209, +9, = 30990= 2499,= 17Step2b)90- 2499, = 17HenceP(t) = +* + t + 249Haco for population in 2020oin PCt)17(30) + 249put t=30P(t) = (30)2P(t)= 333million2030for population input t= 40 in p (t)- (40)a17(40)P(t) =+ 249

Answered: How did you make your system on linear…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

How did you make your system on linear equations? Where did you get the 100? 10? 400? 20?

5:47
Expert Answer
Step1
a)
#17
P(e) = azt + a,t + a.
249 million in
1990
281
million in
2000
309 million
in
2010
at t=o, PC+) = 249
at t=lo, P(t) = 281
at te 20, P(t) = 309
249 = 0+o + 4.
281=a2(100) +9,(10)+ 90
309=0 (400)+a,(20)+9o
a.- 24 9
S1stem 아
equations
(0o aatlo9, +9,= 20
400 92 +209, +9, = 309
90= 249
9,= 17
Step2
b)
90- 249
9, = 17
Hence
P(t) = +* + t + 249
Haco for population in 2020o
in PCt)
17(30) + 249
put t=30
P(t) = (30)2
P(t)= 333
million
2030
for population in
put t= 40 in p (t)
- (40)a
17(40)
P(t) =
+ 249

Expert Solution

Step 1

From the given data,

Population in 1990 is 249 million

Population in 2000 is 281 million

Population in 2010 is 309 million

Let us consider 1990 as initial year. So, it can be considered that at t=0, population is 249 million. At t=10 , population is 281 million and at t=20, population is 309 million.

Let, the population at time t is represented by

$P (t) = a t^{2} + b t + c$ (i)

Where a,b,c are arbitrary constants to be determined

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