practice_test-parametric_equations-solutions.pdf - Math 116...

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Math 116 — Practice for Exam 2Generated October 1, 2017Name:SOLUTIONSInstructor:Section Number:1. This exam has 5 questions. Note that the problems are not of equal difficulty, so you may want to skipover and return to a problem on which you are stuck.2. Do not separate the pages of the exam. If any pages do become separated, write your name on themand point them out to your instructor when you hand in the exam.3. Please read the instructions for each individual exercise carefully.One of the skills being tested onthis exam is your ability to interpret questions, so instructors will not answer questions about examproblems during the exam.4. Show an appropriate amount of work (including appropriate explanation) for each exercise so that thegraders can see not only the answer but also how you obtained it. Include units in your answers whereappropriate.5. 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. Youare also allowed two sides of a 3′′×5′′note card.6. If you use graphs or tables to obtain an answer, be certain to include an explanation and sketch of thegraph, and to write out the entries of the table that you use.7. You must use the methods learned in this course to solve all problems.SemesterExamProblemNamePointsScoreFall 201437chickens vs. robots14Fall 201518boxers213Fall 2016210tracking chip14Winter 201726Venice Beach13Winter 201521spinning16Total70Recommended time (based on points): 67 minutes
Math 116 / Final (December 12, 2014)page 87. [14 points] Chickens continue to appear around you, and Franklin’s army is hesitant to advance.a. [6 points] LetF(t) give the total number of chickens that have arrived aftertseconds.You observe thatF(t) obeys the following differential equationdFdt=eFt2.If there are initially 20 chickens, find a formula (in terms oft) forF(t).
b. [4 points] A large, familiar-looking chicken steps forward from the flock and clucks, “KooKoo Katcha!”.This large chicken waddles towards Franklin following the parametricequationsx(t) =sin(πt) + 1πy(t) = ln(t+ 1)wheretis the time, in seconds, after the chicken steps forward from the flock and bothxandyare measured in feet. Find the chicken’s speed 10 seconds after it steps forward.Include units.
University of Michigan Department of Mathematics

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