Mudassir Lodi

Homework for Lecture 23 of Dr. Z.’s Dynamical Models in Biology class
Email the answers (either as .pdf file and/or .txt file) to ShaloshBEkhad@gmail.com by 8:00pm Monday, Nov. 22,, 2021. Subject: hw23 with an attachment hw23FirstLast.pdf and/or hw23FirstLast.txt
Also please indicate (EITHER way) whether it is OK to post
1.	Carefully read, and understand, the posted solution to the attendance quiz for Lecture 22 https://sites.math.rutgers.edu/~zeilberg/Bio21/att23S.pdf .
For each of the problems that you got wrong, explain what you did wrong, or what you were confused about.
Then for each of the problems that you got wrong, make up two similar ones and solve them.

I did not have enough time to complete all of the questions, but I understood what to do. 

The population of a species changes from one generation to the next. The value at a given generation is three times the value at the previous generation. (Discrete)

x(n) = 3x(n-1)(1-x(n-1))
f(x) = 3x(1-x)
x - 3x(1-x) = 0
{0, 1/3}
f(x) = 3x - 3x^2
f'(x) = 3 - 6x, f'(0) = 3. f'(1/3) = 1
x = 0  is not stable. 
x = 1/3 is stable. 

The population of a certain species is decreasing at a rate that is three times its current value. (Continuous)

x'(t) = -3x(t)
f(x) = -3x
x = 0 is the equilibrium point. 
f'(x) = -3, f'(0) = -3
x = 0 is stable. 

2.	Make progress on your final project, with your team-mates.