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In this problem we examine the phase difference between the cyclic variations of the
Chapter 9, Problem 6(choose chapter or problem)
In this problem we examine the phase difference between the cyclic variations of the predator and prey populations as given by equations (24) of this section. Suppose we assume that K > 0 and that t is measured from the time that the prey population x is a maximum; then = 0. a. Show that the predator population y reaches a maximum at t = /(2 ac) = T/4, where T is the period of the oscillation. b. When is the prey population increasing most rapidly? decreasing most rapidly? a minimum? c. Answer the questions in part b for the predator population. d. Draw a typical elliptic trajectory enclosing the point (c/, a/), and mark on it the points found in parts a, b, and c
Questions & Answers
QUESTION:
In this problem we examine the phase difference between the cyclic variations of the predator and prey populations as given by equations (24) of this section. Suppose we assume that K > 0 and that t is measured from the time that the prey population x is a maximum; then = 0. a. Show that the predator population y reaches a maximum at t = /(2 ac) = T/4, where T is the period of the oscillation. b. When is the prey population increasing most rapidly? decreasing most rapidly? a minimum? c. Answer the questions in part b for the predator population. d. Draw a typical elliptic trajectory enclosing the point (c/, a/), and mark on it the points found in parts a, b, and c
ANSWER:Step 1 of 5
a)
The equations are given as
From the 
We know that the maximum value for the same functions is 1 . We are only interested in the predator population 
Since we have
The sine function reaches its maximum for 
