> #HW 23 #Timothy Nasralla, 11/22/21
> #Question 1: I seemingly didn't get any questions wrong, however I did not
> make it to last question due to time
> #The population of a certain species scaled such that it is increasing at a
> rate that was three times its current value times (1 - 0.5* its current
> value).
> #This would be continuous time # x'(t) = 3*x(t) * (1 - 0.5*x(t) # f(z) = 3*z *
> (1 - 0.5*z). # Solving for f(z) = 0, z can be 0 or 2. # f'(z) = 3 - 3*z. If z
> = 0, f'(z) is 3 which is positive and not stable. If z = 2, f'(z) is -6 whihc
> is negative and therefore stable.
> #The population of a certain species scaled such that it is decreasing at a
> rate that was 2.5 times its current value times (1 - its current value).
> #This would be continuous time # x'(t) = 2.5*x(t) * (1 - x(t) # f(z) = 2.5 *z
> * (1 - z). # Solving for f(z) = 0, z can be 0 or 1. # f'(z) = 2.5 - 5*z. If z
> = 0, f'(z) is 2.5 which is positive and not stable. If z = 1, f'(z) is -2.5
> whihc is negative and therefore stable.