B) In the study of population dynamics, one of the most famous models for limited population growth is the equation logistics: dP dt P(a - bp) where, a, b are positive constants. Solve the differential equation above. (Hint: Consider Bernoulli's equation.)

dv A model for the velocity v at timetof a certain object faling under the influence cf gravity in a viscous medium is given by the equation 1-. From the direction field shown in the figure to the right, skotch the dt 12 solutions with the initial conditions v(0) = 10, 12, and 19. Why is the value v= 12 calied the "terminal velocity"? Choose the correct skelch of the solutions with the initial conditions v(0) = 10, 12, and 19. O A. OB. Oc.

2. Consider a logistic equation: dN N 2(1 - dt with the initial population No = 2. Find the solution N(t).

How to solve the differential equation and draw the phase diagram?