# HW7 - [1 73.11904 The population reduced when we changed...

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I: Population dynamics - Logistic Growth model: Question #1 -------R code------ Nt=2; r=0.05; K=10000; DN=r*Nt*(1-Nt/K) Nt1=Nt+r*Nt*(1-Nt/K) population<-c(2) i=2 for ( j in c(1:99)) { Nt1=Nt+r*Nt*(1-Nt/K) population[i]=Nt1 i=i+1 Nt=Nt1 } plot(population) title(main = "Population curve with Nt=2; r=0.05; K=1000;") Nt=2; r=0.05; K=1000; DN=r*Nt*(1-Nt/K) Nt1=Nt+r*Nt*(1-Nt/K) population<-c(2) i=2 for ( j in c(1:99)) { Nt1=Nt+r*Nt*(1-Nt/K) population[i]=Nt1 i=i+1 Nt=Nt1 } Population_at_the_End_Of_100 th _Year_For_K_1000=Nt

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Nt=2; r=0.05; K=100; DN=r*Nt*(1-Nt/K) Nt1=Nt+r*Nt*(1-Nt/K) population<-c(2) i=2 for ( j in c(1:99)) { Nt1=Nt+r*Nt*(1-Nt/K) population[i]=Nt1 i=i+1 Nt=Nt1 } Population_at_the_End_Of_100 th _Year_For_K_100=Nt; Population_at_the_End_Of_100 th _Year_For_K_1000 Population_at_the_End_Of_100 th _Year_For_K_100 ------R Output-------
Population_at_the_End_Of_100th_Year_For_K_1000 [1] 202.3481 Population_at_the_End_Of_100th_Year_For_K_100

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Unformatted text preview: [1] 73.11904 The population reduced when we changed the value of K from 100o to 100 Question #2-------R code------Nt=1000; r=0.05; K=200; DN=r*Nt*(1-Nt/K) Nt1=Nt+r*Nt*(1-Nt/K) population<-c(1000); i=2 for ( j in c(1:100)) { Nt1=Nt+r*Nt*(1-Nt/K) population[i]=Nt1; i=i+1; Nt=Nt1; } plot(population) title(main = "Population curve with Nt=1000; r=0.05; K=200;")------R Output---------From the graph, it’s clear that the saturation will be around 60 years. Question #3-------R code------Nt=6; r=0.019; K=11; Nt1=Nt+r*Nt*(1-Nt/K) population<-c(6) i=2 while (Nt<=10) { Nt1=Nt+r*Nt*(1-Nt/K) population[i]=Nt1 i=i+1 Nt=Nt1 } i Required_Years=i-2 Required_Years Nt--------R Output----------> Required_Years [1] 112 > Nt [1] 10.01653 So the population will be around 10 billion by 1997+112=2109...
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## This note was uploaded on 07/11/2011 for the course ELECTRICAL EE101 taught by Professor S.dpal during the Spring '11 term at IIT Kanpur.

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HW7 - [1 73.11904 The population reduced when we changed...

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