Math 103 Exam 2 October 29 2019 Name Student ID Indicate your section instructor cid 3 001 Frank Zimmitti cid 3 003 Robert Huben cid 3 005 Leilani Pai cid 3 007 Matthew Bachmann cid 3 008 Ben Drabkin cid 3 009 Ana Wright Steve Eckman cid 3 181 cid 3 002 Catherine Zimmitti cid 3 004 cid 3 006 Dylan McKnight Juliana Bukoski Jake Kettinger cid 3 101 103 Answer the questions in the spaces provided on the question sheets Show an appropriate amount of work including appropriate explanation for each problem so that graders can see not only your answer but also how you obtained it Include units in your answer when possible You may receive 0 points for a problem where you show no work Instructions 1 Do not open this exam until you are told to do so 7 Do not separate the pages of this exam If they do become separated point this out to your instructor when you hand in the exam 2 Write your initials on every page 8 Make sure your answer is clearly marked 3 No books or notes may be used on the exam 4 You may only use an approved calculator on the exam If you have a problem with your calculator raise your hand 5 Read and follow directions carefully 6 All cell phones must be turned off and put away during the exam Any device that connects to a phone or the web must be removed and put away 9 Credit or partial credit will be given only when the appropriate explanation and or work is shown 10 This exam has 10 questions for a total of 100 points There are 10 pages besides this one 11 You will have 90 minutes to complete the exam 12 If you use graphs or tables to nd an answer be sureto include an explanation and sketch of the graph and to write out the entries of the table that you use You can use this page for scratch work 1 9 points Recall the following properties of natural logarithms 1 ln eA A 2 ln A B ln A ln B 3 ln AB B ln A 4 eln A A cid 18 A cid 19 B 5 ln ln A ln B Initials 6 The equation ln x A is equivalent to eA x Solve the following expressions for x exactly no decimal approximations When you use one of the properties above make a clear note of the number of the property that you are using You must show work to receive credit a ln x2 ln x6 16 b ln 4 ex 9 c ln 3x 5 7 1 2 Page 2 2 10 points A sample of a radioactive element is buried The amount of the element in kilograms remaining t years after 2019 is given by the equation a Evaluate and interpret f 100 Show your work Write your answer in a complete sentence with units f t 1500e 0 011t Initials b Evaluate and interpret f 1 200 Show your work Write your answer in a complete sentence with units c Calculate the half life of this element Show your work Write your answer in a complete sentence with units Page 3 3 9 points This question uses the following three functions f x log x 7 g x 2x 1 and h x x3 x2 Initials a Evaluate f g 6 b Find a formula for h g x c Find a formula for f 1 x Page 4 4 12 points a Consider the graph of y x2 3x Find a formula for the function you would get after shifting this graph to the left 5 units Initials b Let g x be a function What transformations have been done to g x in order to obtain the graph of the function 2g x 7 Be speci c about stretch compression factors and shift amounts and clearly indicate the order that the transformations are applied c Suppose that the graph of h x contains the point 3 5 What point must be on the graph of h 2x Page 5 Initials 1 1 y y 1 1 x x 5 12 points The graph of a function g x is given below y 4 3 2 1 4 3 2 1 1 2 3 4 1 2 3 4 x a Graph the function g x 2 You do not need to ll in both sets of axes but make sure your nal answer Graph of g x is on the rightmost set of axes y You may use this graph for scratch work Graph of g x 2 b Graph the function g 2x 1 You do not need to ll in both sets of axes but make sure your nal answer is on the rightmost set of axes y You may use this graph for scratch work Graph of g 2x 1 1 1 1 1 x x Page 6 6 6 points Find a formula for the quadratic f x graphed below Initials 5 4 3 2 1 1 2 3 4 1 2 3 4 5 Graph of f x 7 6 points The Great Galumbo is red out of a cannon as part of their circus act on Mars Let h t denote their height in meters t seconds after the cannon launches them Suppose the cannon starts on a platform 3 meters off the ground and The Great Galumbo reaches their highest point of 11 meters off the ground 2 seconds after being red Find a formula for the quadratic function h t Page 7 8 12 points a What are the roots of f x 9x2 x 4 3 x 1 2 What is the multiplicity of each root Initials b What is the degree of g x 6x4 7x3 9x 8 c What is the leading coef cient of g x 6x4 7x3 9x 8 d Fill in the blanks to describe the long run behavior of h x 5x7 As x h x As x h x Page 8 9 12 points Parts a b and c deal with the rational function f x graphed below Initials 5 4 3 2 1 2 1 1 2 3 4 5 x f x 5 4 3 2 1 1 2 3 4 5 Graph of f x a Does the function f x have any zeros If so list out all zeros If not explain why there are no zeros b Does the function f x have any vertical asymptotes If so list out all vertical asymptotes If not explain why there are no vertical asymptotes c Does the function f x have any holes If so list out all holes If not explain why there are no holes Part d deals with the rational function g x graphed below g x d Find a possible formula for g x 5 4 3 2 1 2 1 1 2 3 4 5 x Graph of g x Page 9 10 12 points Use the six graphs of the functions below to answer the following …