Consider the survival of a population of whales and assume that if the number of whales falls below a minimum survival level m, then the species will become extinct. In addition, assume that the population is limited by the carrying capacity M of the environment. The following model is proposed to describe this population: w(t + 1) = w(t) + k(M - w(t)) (w(t) - m),
where k > 0.
a. Does this model make sense in terms of the description above? Explain.
b. Find the equilibria of the model and determine their stability.
c. Perform a graphical equilibrium and stability analysis assuming that M = 5000, m = 100, k = 0.0001. (Use Matlab or a graphing calculator to graph the right-hand side of the model.) Compare your results to the general case under b).
d. The model has two serious shortcomings. What are they? (Consider what happens if w(0) < m, or when w(0) is much larger than M.)

answer: f true

step-by-step explanation:

answer: two angles are called supplementary if they add up to 180°. example: the two angles (140° and 40°) are supplementary because they add up to 180°.

step-by-step explanation:

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation:

3 ft is your answer