Differential Equations

Question

Consider the rate of change equation dy/dt = 0.5y(2+y)(y-8) which has been created to
provide predictions about the future population of rabbits over time.

 

a) For what values of y is y(t) increasing? Explain your reasoning.

b) For what values of y is y(t) decreasing? Explain your reasoning.
c) For what values of y is dy/dt neither positive nor negative? What does this imply about the
solution function y(t)?

 

Answer 1

Increasing on (-infinity,-1.055) and (5.055,infinity)

Decreasing on (-1.055,5.055)

zero at x=0,-2,and 8