Please help with the following questions:

12. (AR) During a chemical reaction, 9 = f[t) models the amount of a substance present, in grams, at time t seconds. At the start of the reaction t = 0, there are 10 grams of the substance present. The function y : t) satises the d differential equation 65: = 0.02y2' (a) Use the line tangent to the graph of y : t) at t = 0 to approximate the amount of the substance at time t = 2 seconds. (b) Using the given dierential equation, determine whether the graph of f could resemble the following graph. t (J (c) Solve y : t) given that n) : 10. (d) Determine if the amount of the substance is changing at an increasing or decreasing rate. 1. (AP). 28. The function N satisfies the logistic differential equation dNV N N dt 10 850 where N(0) = 105. Which of the following statements is false? (A) lim N(t) = 850 1-700 dN (B) dt has a maximum value when / = 105. (C) d+ 2 -= 0 when N = 425. (D) When N > 425, dN d'N dt > 0 and d12 50. 2. (AP.) 27. The number of students in a cafeteria is modeled by the function P that satisfies the logistic differential dP 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? (A) 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 dt 3 2100 where t is measured in years for t 2 0 and P(0) = 400. Which of the following statements could be true? 1. lim P (t) > 1150 Il. The graph of P has a point of inflection for t > 0. Ill. The maximum rate of change of P occurs at t = 0. (A) None B II only C I and II only D Il and Ill only 4. (AP.) The rate of change, -, 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 time, 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? A de = (500 - P) B dt = 30 P (500 - P) C dP = 300 P (500 - P) D "= 1206 P (500 + P)