a   The population of a certain species is decreasing at a rate that is twice its current value.

i)                   Continuous-time dynamical model

ii)                 y = x – x^2

iii)               

iv)                 

b   The population of a certain species changes from one generation to the next. The value at a given generation is one-half of its value at the previous generation.

i)                   Discrete-time dynamical model

ii)                 X(t) = x

                Y(t) = (1/2)x(t)

iii)               Y = (1/2)x

c    The population of a certain species changes from one generation to the next. The value at a given generation is twice its value at the previous generation times (1 minus its value at the previous generation).

i)                   Discrete-time dynamical model

d   The population of a certain species scaled such that the maximum possible is 1 is increasing at a rate that is twice its current value times (1 minus its current value).

i)                   Continuous-time dynamical model

ii)                 Y = x^2