Math 103 Benchmark 2 March 29 2023 Name Student ID Indicate your section instructor 002 004 David Lieberman Sara McKnight 003 Valerie Morris 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 2 Write your initials on every page 3 Write your answers in boxes when provided 4 No books or notes may be used on the exam 5 You may only use an approved calculator on the exam Graphing calculators are not allowed If you have a problem with your calculator raise your hand 6 Read and follow directions carefully 8 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 9 Make sure your answer is clearly marked 10 Credit or partial credit will be given only when the appropriate explanation and or work is shown 11 This exam has 8 questions for a total of 50 points There are 7 pages besides this one 12 You will have 90 minutes to complete the exam 7 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 13 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 You can use this page for scratch work cid 16 cid 17 nt r n A t P 1 Quadratic Formula Equation Sheet A t Pert b x b2 4ac 2a Initials A t P 1 r t 1 6 points Suppose that a bowling alley brings in 300 in revenue for each hour they are open a Write an equation for R h the revenue the bowling alley brings in after being open for h hours b It costs the bowling alley C h 150h 2500 to be open for h hours Write an equation for the profit P h after being open for h hours Page 2 2 7 points The amount of thorium in a sample is given by the equation A t 5e 0 0288t where t is measured in days and A t is measured in grams a What is the continuous decay rate per day of thorium Initials b What is the effective percent decay rate per day of thorium c What is the half life of thorium Page 3 3 6 points Write an equation for the power function f x kxp which passes through the points 1 6 and 3 162 Initials 4 6 points Use properties of logarithms to solve log10 x2 log10 3 for x cid 17 cid 16 8 x4 Page 4 5 6 points Below is the graph of f x Initials y 1 1 x Match each of the following graphs to one of the functions below a g x 1 Graph A Graph B Graph C Graph D 2 f x 1 b h x f 2x 3 Graph A Graph B Graph C Graph D c i x f x 1 2 Graph A Graph B Graph C Graph D d j x 2 f x 4 Graph A Graph B Graph C Graph D y 1 1 1 1 Graph A y x x y 1 1 1 1 Graph B y x x Graph C Graph D Page 5 6 7 points Consider a function f x Suppose another function g x is given by g x 2 f cid 0 1 Initials 3 x 1 cid 1 6 Describe the graph of g x as the result of applying shifts reflections stretches and compressions to the graph of f x Be careful about the order of transformations 7 6 points On the planet Mars you throw a ball from the top of a hill Its height above the ground in meters t seconds after being thrown is given by the function h t 2t2 40t 250 a What is the maximum height achieved by the ball b When will the ball hit the ground Page 6 8 6 points a Write the following quadratic equation in vertex form f x 2x2 10x 3 Initials b Write an equation for the function whose graph is the parabola shown below y 1 1 x Page 7