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Consider the differential equation - ap dt = - p(p - 1.25)(p - 2.5) for the population p (in thousands) of a certain species at time t. Complete parts (a) through (e) below. (a) Sketch the direction field by using either a computer software package or the method of isoclines. Choose the correct sketch below. OA. O B. O C. Q (b) If the initial population is 3400 [that is, p(0) = 3.4], what can be said about the limiting population lim p(t)? 1+ + 00 If p(0) = 3.4, then lim p(t) = . The population will 1-+ 00 (c) If p(0) = 2.4, what can be said about the limiting population lim p(t)? 1 - + 00 If p(0) = 2.4, then lim p(t) = . The population will 1 - + 00 (d) If p(0) = 0.9, what can be said about the limiting population lim p(t)? 1+00 If p(0) = 0.9, then lim p(t) = . The population will 1- + 00 (e) Can a population of 4000 ever decline to 1400? it V possible for a population of 4000 to decline to 1400. One solution of the given differential equation is the horizontal line p(t) = . If the population were to decline from 4000 to 1400, the corresponding solution curve would that horizontal line. This would what is guaranteed by the existence-uniqueness theorem