Answer Happy

for part c use p(0)=1.2
The direction field for oxy is shown to thenght (a) Verily that the straight lines y txare solution curves, provided b) Such the solution with initial constion yo-2 Sketch the solution curve within condition 1 (d) What can be said about the behavior of the above solutions + +0. How out ? is not defined when you the times one at a timely in the the standards of international The recto y meded tec Smally your one Substituting the Westion for at the differentiaquation wide
dp The logistic equation for the population in thousands) of a certain species is given by = 7p-4p. Complete parts (a) through (d) below. (a) Sketch the direction field by using either a computer software package or the method of isoclines. Choose the correct sketch below. Ос. . (b) If the initial population is 2000 (that is, p(0) = 2}, what can be said about the limiting population lim put/? i plo) = 2, then lim p(1) The population will (c) If p(0) = 1.6, what can be said about the limiting population lim piti? If p(0) = 1.6. then lim p(t) = 0. The population will (d) Can a population of 2000 ever decline to 1600? possible for a population of 2000 to decline to 1600. One solution of the given differential equation is the horizontal line p(t) = | 1. If the population were to decline from 2000 to 1600, the corresponding solution curve would that horizontal line. This would what is guaranteed by the existence uniqueness theorom.