Module 2: AuthenticAssessment Graphs of Polynomial and Rational Functions (3 pages) Directions: Using your knowledge of polynomial and rational functions, provide the correct answers to the following scenarios and questions. Make sure to completely answer each question and to show all of your work. | Part 1: Rocket Flight Pretend that with a stopwatch and a video camera, you recorded the flight of a miniature firework rocket. As the rocket stood upright on the ground (hy), you lit the fuse and the rocket traveled along a path in the shape of a parabola, hitting the ground (t5) again exactly 7 seconds later. lllllllllllllllm' As you may recall, & (in feet) of a short range rocket, as a function of time, , (in seconds) after liftoff from an initial height, hy, may be modeled by the polynomial function h(t) = 16t% + vyt + hy. Another way to express this height function is h(t) = 16(t)(t ty) + hg, where ty is the time elapsed after liftoff until the rocket returns to ground (where /=0 again). Using the data you gathered, and the modeling equations above, answer the following equations: 1. Determine the height equation for your rocket. (1 point) 2. Sketch a graph of the function, labeling each axis. (1 point) 3. At what time(s) will the rocket be at a height of 192 feet? (1 point) 4. What is the rocket's maximum height? At what time does the rocket reach its maximum height? (2 points) Part 2: Population Growth Pretend that the local marine commission placed 100 seed oysters in a large estuary to begin a commercial oyster farm. The commission's scientists estimate the oyster population P growth within the estuary years after the initial placement to be: 40(4.85t + 2.5) PO ="8t+D 1. What type of function is the population function? Why? (2 points) 2. Create a table of values for 0