Pleas help with following problems with the context provided:

Logistic Differential Equations dt dy = k(L - y)y ( or at dy = k(1 - " ) y) . k: constant of proportionality . L: carrying capacity Remarks. . If y 0. . If y > L then dy/ dt co dN (B) - has a maximum value when N = 105. dt (C) = 0 when N = 425. dt2 (D) When N > 425, - dN dt - > 0 and d-N dt2 2. (AP.) 27. The number of students in a cafeteria is modeled by the function P that satisfies the logistic differential dp 1 equation - dt 2000 - P(200 - P), where t is the time in seconds and P(0) = 25. What is the greatest rate of change, in students per second, of the number of students in the cafeteria? 5 (B) 25 (C) 100 (D) 2003. The size of a bird population is modeled by the function P that is a solution to the logistic differential equation dP_P P2 E 3 2100' where t is measured in years for t 2 D and 13(0) = 400. Which of the following statements could be true? It fhump) 1150 II. The graph of P has a point of inection fort > 0. III. The maximum role of change of P occurs alt 0. None ll only land l| only II and Ill only 4. (AR) ("3 The rate of change, 5' of the number of people entering a movie theater is modeled by a logistic differential equa- tion. The capacity of the theater is 500 people. At a certain time1 the number of people in the theater is 100 and is increasing at the rate of 50 per minute. Which of the following differential equations could describe this situation? % 550013) 'fo:%P(BOOiP) "P = 413(500 P) d! 800 6) "P : 4P(500+P) d: 1200