Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function c(t) = 181 + 541 (2 +71+10' , where the time, t is hours after injection. Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. (5 points) Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body. (5 points)A polynomial f(x) has the given zeros of B, 'l, and 3. Part A: Using the Factor Theorem, determine the polynomial f (X) in expanded form. Show all necessary calculations. (3 points) Part B: Divide the polynomial f (x) by (x2 x 2) to create a rational function g(x) in simplest factored form. Determine g(x) and nd its slant asymptote. (4 points) Part C: List all locations and types of discontinuities of the function g(x). (3 points) A railroad's track can be determined using the following graph, Several different roadways are in the same region as the railroad, Part A: A highway's path can be found using the equation 2): + 3y = 18 Use the graphs of the functions to determine the number of intersections there will be between the railroad and the highway, and explain completely. (5 points) Part B: A turnpike's route is determined by the equation 3. = gxz' Prove algebraically how many intersections there will be between the railroad and the turnpike, showing all necessary work. (5 points) An ice cube is freezing in such a way that the side length 5, in inches. is 5\") = ins. where tis in hours. The surface area of the ice cube is the function A(s) = 652. Part A: Write an equation that gives the volume att hours after freezing begins. (2 points} Part B: Find the surface area as a function of time, using composition. and determine its range. (4 points) Part C: After how many hours will the surface area equal 384 square inches? Show all necessary calculations. (4 points)