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: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

the 8 in 8,420 is in the thousands place so it's value is 8 thousand.

the 8 in 6,870 is in the hundreds place so it's value is 8 hundred.

divide 8000 by 800 to find the answer:

8000 / 800 = 10

the 8 in 8,420 is 10 times greater than the 8 in 6,870

the answer is c

step-by-step explanation: i took a test with this question on it

the given growth  function for the length of the fish (cm) is

f(m) = 5(1.07)m = 5.35m

where 

m = months

at the end of the study, the length is 9.19 cm. the  time for conducting the study is determined as

5.35m = 9.19

m = 1.7178 months

part a.

the study was performed over a time period  of about 1.72 months. therefore  the domain for  plotting the function is 0 < = m < = 1.72.

note:

if growth  continues at this rate for up to m months, then the domain would be 0< =m< =m.

part b.

the growth function is a linear function.

when m=0, f=0.

therefore the initial growth is zero, which represents the y-intercept.

part c.

assume that the growth function is valid for 0< =m< =9.

the average rate of change of the function is the slope of the linear function, which is 5.35 cm/month.