FinalF10_Solns - Math 105 Final Exam December 17, 2010...

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Math 105 — Final Exam December 17, 2010 Name: EXAM SOLUTIONS Instructor: Section: 1. Do not open this exam until you are told to do so. 2. This exam has 13 pages including this cover. There are 10 problems. Note that the problems are not of equal diFculty, 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. 7. If you use graphs or tables to ±nd 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 of all cell phones and pagers , and remove all headphones. Problem Points Score 1 10 2 10 3 18 4 9 5 5 6 5 7 9 8 10 9 14 10 10 Total 100
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Math 105 / Final (December 17, 2010) page 2 1 . [10 points] For each statement below, circle True if the statement is always true. Otherwise, circle False . You do not have to show any work for your answers. a . [2 points] If f is an invertible function and f (5) = 2, then f - 1 (5) = 1 2 . True False b . [2 points] If h is an invertible function, then the domain of h - 1 is the range of h . True False c . [2 points] If a radioactive substance decays 25% every year, then its half-life is two years. True False d . [2 points] The function f ( x ) = e 2 x + 1 is a linear function. True False e . [2 points] The line y = 4 is a horizontal asymptote of the function y = f ( x ) = 3 - 5 x 2 + 4 x x + 2 . True False
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Math 105 / Final (December 17, 2010) page 3 2 . [10 points] a . [5 points] A portion of the graph of a power function q ( x ) is shown below. Find a formula for q ( x ). x (1 , 9) (3 , 1 3 ) y = q ( x ) y Solution: Because we are told q ( x ) is a power function, we know that q ( x ) = kx p for some constants k and p . Inserting the point (1 , 9) into the equation, we get 9 = k 1 p = k, so k = 9. Now using the second point, 1 3 = 9(3) p 1 27 = 3 p ln( 1 27 ) = p ln(3) So p = ln( 1 27 ) / ln(3) = - 3. Answer:
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FinalF10_Solns - Math 105 Final Exam December 17, 2010...

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