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Unformatted text preview: Math 115 Second Midterm November 15, 2011 Name: EXAM SOLUTIONS Instructor: Section: 1. Do not open this exam until you are told to do so. 2. This exam has 9 pages including this cover. There are 9 problems. Note that the problems are not of equal difficulty, so you may want to skip over and return to a problem on which you are stuck. 3. Do not separate the pages of this exam. If they do become separated, write your name on every page and point this out to your instructor when you hand in the exam. 4. Please read the instructions for each individual problem carefully. One of the skills being tested on this exam is your ability to interpret mathematical questions, so instructors will not answer questions about exam problems during the exam. 5. Show an appropriate amount of work (including appropriate explanation) for each problem, so that graders can see not only your answer but how you obtained it. Include units in your answer where that is appropriate. 6. You may use any calculator except a TI-92 (or other calculator with a full alphanumeric keypad). However, you must show work for any calculation which we have learned how to do in this course. You are also allowed two sides of a 3 5 note card. 7. If you use graphs or tables to find an answer, be sure to include an explanation and sketch of the graph, and to write out the entries of the table that you use. 8. Turn off all cell phones and pagers , and remove all headphones. 9. You must use the methods learned in this course to solve all problems. 10. You must clearly indicate your final answer for each problem to receive credit. Problem Points Score 1 9 2 8 3 12 4 10 5 8 6 13 7 16 8 12 9 12 Total 100 Math 115 / Exam 2 (November 15, 2011) page 2 1 . [9 points] Let U = f ( t ) give the number of Facebook users in millions in year t . Suppose f (2005) = 5 . 5 and f (2005) = 4 . 9. For this problem assume that f ( t ) is strictly increasing. a . [4 points] Find and interpret, in practical terms, f 1 (5 . 5). Solution: The year in which there were 5.5 million Facebook users was 2005. f 1 (5 . 5) = 2005 (year) b . [5 points] Showing work, evaluate ( f 1 ) (5 . 5). Interpret your answer in practical terms. Solution: ( f 1 ) (5 . 5) = 1 / ( f ( f 1 (5 . 5)) = 1 /f (2005) = 1 / 4 . 9 . When the number of Facebook users was 5.5 million, in 1/4.9 ( 0.2) years the number of Facebook users will have increased by approximately 1 million users. ( f 1 ) (5 . 5) = 1 / 4 . 9 years per million users 2 . [8 points] Recall the function T ( x ) that took the number of followers (in millions) of a Twitter user and returned a value from 0 to 10 called the users Twitter celebrity index. The derivative of T ( x ) is given by the function T ( x ) = 1532 . 5 (0 . 6) x (5 + 60(0 . 6) x ) 2 ....
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This note was uploaded on 01/28/2012 for the course MATH 115 taught by Professor Blakelock during the Fall '08 term at University of Michigan.
- Fall '08