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Unformatted text preview: Math 116 Final Exam December 15, 2005 Name: Instructor: Section Number: 1. Do not open this exam until you are told to begin. 2. This exam has 11 pages including this cover. There are 9 questions. 3. Do not separate the pages of the exam. If any pages do become separated, write your name on them and point them out to your instructor when you turn in the exam. 4. Please read the instructions for each individual exercise carefully. One of the skills being tested on this exam is your ability to interpret questions, so instructors will not answer questions about exam problems during the exam. 5. Show an appropriate amount of work for each exercise so that the graders can see not only the answer but also how you obtained it. Include units in your answers where appropriate. 6. You may use your calculator. You are also allowed two sides of a 3 by 5 notecard. 7. If you use graphs or tables to obtain an answer, be certain to provide an explanation and sketch of the graph to make clear how you arrived at your solution. 8. Please turn off all cell phones and remove all headphones. Problem Points Score 1 12 2 10 3 9 4 8 5 12 6 18 7 12 8 9 9 10 Total 100 2 1. (12 points) The world shrimp production can be represented by the differential equation dP dt =- . 1 P ( P- 7) , where t is the number of years since 1982 and P ( t ) is the quantity of shrimp farmed in the world during year t in hundreds of thousands of metric tons. In 1982 the world shrimp production was 100,000 metric tons. (a) (3 pts.) Determine all of the equilibrium solutions of the differential equation given above. Classify each as either stable or unstable. No explanation required. (b) (4 pts.) Sketch a graph of the solution to the given initial value problem. Be sure to indicate clearly on your graph where the solution curve is increasing/decreasing and where it is concave up/concave down. Clearly mark the value of any asymptotes....
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- Winter '08