1. (07.07 HC) A certain bacteria grows according to the function P. Consider P a solution to the logistic differential equation g = APP-L]. where P is 7000 the pepulation of bacteria and t is measured in days. Part A: If P(O) = 2,400, solve for P(t). (10 points) Part B: What is the largest rate of increase in the number of bacteria? (1 0 points) Part C: What will be the maximum number of bacteria? Explain your reasoning. (10 points) B i Q FontFamin 'AA' A .0 FvE v55 v c:) y lg n n. g 14 g 2. (04.05. 05.04, 07.04 HC) ConSIder the differential equation a = 3(2): +0an + x+ 3). Part A: Find the equation of the line tangent to the solution curve at the point (0, 3). (5 points) Part B: Find the second derivative at (U, 3) and use it to determine the concavity of the solution curve at that point. Explain. (1 0 points) Part C: Find the particular solution y = f(x) with initial condition f(0) = 3. (15 points) 3. (07.05 HC) Newton's Law of Cooling states that the rate of change of the temperature of an object. T. is proportional to the difference of T and the temperature of its surrounding environment. A pot of chili with temperature 26C is placed into a -13C freezer. After 2 hours, the temperature of the chili is 8C. Part A: Assuming the temperature T of the chili follows Newton's Law of Cooling, write a differential equation for T. (10 points) Part B: What is the temperature of the chili after 4 hours? (20 points) Part C: At what time, t, will the chili's temperature be -5C? (10 points)