Question

The number of fish per square kilometer in a lake is determined by the DTDS

xt+1=400xt200+0.1xt ,

where t is the time in years since the beginning of the observation. The initial observation is of 2,100 fish per square kilometer.

a) How many fish per square kilometer will there be after three years? Give your answer with an accuracy of two decimal places.

Answer:      

b) Find the updating function f.

Answer: f(x)=    

c) Find the inverse of the updating function.

Answer: f−1(x)=    

d) How many fish per square kilometer were there one year before the initial observation? Give your answer with an accuracy of two decimal places.

Answer:     

e) Find the two equilibria of this system. Separate each value by a semi-colon.

Answer:      

f) Compute the derivative f′ of f.

Answer f′(x)=    

g) If p1<p2 are the two equilibria, compute the values of f′(p1) and f′(p2). Give exact answers.

Answer: f′(p1)=    

                f′(p2)=    

h) Determine the stability of each equilibrium.

Answer: p1 is   

		unstable
		stable

   because

		f′(p1)>0
		|f′(p1)|<1
		|f′(p1)|>1
		f′(p1)<0
		|f′(p1)|=1
		f′(p1)=0

  p2 is  

		unstable
		stable

  because   

		f′(p2)>0
		f′(p2)=0
		|f′(p2)|=1
		|f′(p2)|<1
		|f′(p2)|>1
		f′(p2)<0

Answer 1

Pls, comment if any issue.