Answers to the Math 336 Final
Rename this file
NikitaJohnFinal.txt
and mail to ShaloshBEkhad@gmail.com no later than Tue., Dec. 14, 2021.


MY NAME: Nikita John

MY RUID: 184005567


Ans. to 1: 1.618033989

Ans. to 2(a): Equilibrium Points: {0, 1, 2}  
Ans. to 2(b): Stable Equilibrium Point: {1}
Ans. to 2(c): x(100) = 0.9999999


Ans. to 3(a): Equilibrium Points: {0, 0.475304923, 2.524695077} 
Ans. to 3(b): Stable Equilibrium Point: {0.475304923} 
Ans. to 3(c): x(1000) = 0.4753049232 

Ans. to 4(a): Proportion of second generation with Aa: 0.5 
Ans. to 4(b): Proportion of 1000th generation with Aa: 0.5                                    


Ans. to 5(a): Proportion of second generation with Aa: 0.4986 
Ans. to 5(b): Proportion of 1000th generation with Aa: 0.3975                                   

Ans. to 6: y(100000000000000000000000000000000000000000000000000000000000) = 0.7478789082

Ans. to 7(a): 5 removed individuals (1000 - 995 - 0) 
	**NOTE: For (a) and (b) I have an extensive explanation of my answers in the pdf file. 
	They are towards the bottom, as 7 was the last question I completed 
Ans. to 7(b): 245 removed individuals (1000 - 735 - 16) 
Ans. to 7(c): beta = mu/N = 100/1000 = 0.1                    


Ans. to 8(a): The height of the horizontal asymptote is at t = 0.6823278038 
Ans. to 8(b): Yes, you get another horizontal asymptote, this time at t = 1.213411663 
Ans. to 8(c): The value at which the equation is last stable is 7.39, and the horizontal asymptote is at t = 1.777163792

Ans. to 9(a): Value of Bacterial Population Density after a long time: 5.083019282 
Ans. to 9(b): Value of Nutrient Concentration after a very long time: 0.6667361650

Ans. to 10(a): Probability of being at site 1 after a long period of time: 0.0769230769230801 
Ans. to 10(b): Probability of being at site 9 after a long period of time: 0.153846153846160