FinalW09_Solns - Math 105 Final Exam April 23, 2009 Name:...

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Unformatted text preview: Math 105 Final Exam April 23, 2009 Name: EXAM SOLUTIONS Instructor: Section: 1. Do not open this exam until you are told to do so. 2. This exam has 11 pages including this cover. There are 10 problems. Note that the problems are not of equal difficulty, and it may be to your advantage to skip over and come back 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 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. Problem Points Score 1 10 2 8 3 5 4 10 5 12 6 11 7 13 8 9 9 12 10 10 Total 100 Math 105 / Final (April 23, 2009) page 2 1 . [10 points] For each statement below, circle TRUE if the statement is always true; otherwise, circle FALSE. No partial credit on this page. For each of the problems on this page, a,b, and k are positive constants. a . [2 points] Suppose the function f ( x ) is defined as follows: f ( x ) = ae x- x 2 e kx + 2 . Then f ( x ) has a horizontal asymptote at y = a . True False b . [2 points] x 1 / 10 < log(10 x ) for all x > 2. True False c . [2 points] ln( x + a ) + b ln( x + a ) = ln( x + a ) ( b +1) True False d . [2 points] If m ( x ) is an invertible function, then g ( x ) = am ( bx ) is also an invertible function. True False e . [2 points] If n ( x ) is an even function, then h ( x ) = n ( x + a ) cannot be an even function. True False Math 105 / Final (April 23, 2009) page 3 2 . [8 points] For each of the following scenarios, find a formula that mathematically models the situation. You do not need to show your work for this page. a . [2 points] Chelsea invests $700 in an account that earns 8.2% interest annually. Find a formula for C ( t ), the amount of money Chelsea has in her account t years after she originally invested. C ( t ) = 700(1 . 082) t b . [2 points] When first planted in Amys yard, a maple tree was measured to be 6 feet tall....
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FinalW09_Solns - Math 105 Final Exam April 23, 2009 Name:...

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