Exam_2_Solns precalc - MATH 105 SECOND MIDTERM EXAM NAME...

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MATH 105 — SECOND MIDTERM EXAM March 18, 2008 NAME: INSTRUCTOR: SECTION NO: 1. Do not open this exam until you are told to begin. 2. This exam has 10 pages including this cover. There are 9 questions. 3. Do not separate the pages of the exam. If any pages do become separated, write your name on them and point them out to your instructor when you turn in the exam. 4. Please read the instructions for each individual exercise carefully. One of the skills being tested on this exam is your ability to interpret questions, so instructors will not answer questions about exam problems during the exam. 5. Show an appropriate amount of work for each exercise so that the graders can see not only the answer but also how you obtained it. Include units in your answers where appropriate. 6. You may use your calculator, but all work must be shown. 7. If you use graphs or tables to obtain an answer, be certain to provide an explanation and sketch of the graph to make clear how you arrived at your solution. 8. Please turn off all cell phones and other sound devices, and remove all headphones. PROBLEM POINTS SCORE 1 12 2 6 3 8 4 12 5 12 6 12 7 12 8 14 9 12 TOTAL 100
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2 1. (3 points each) Circle “True” if the statement is true and “False” if the statement is false. Then state the exact range of each function. (a) If the domain of f ( x ) = e x is taken to be −∞ < x < , then f is an invertible function. True False Range: 0 < y < (b) If the domain of f ( x ) = e x is taken to be 0 < x < , then f is an invertible function. True False Range: 1 < y < (c) If the domain of f ( x ) = ln( x ) is taken to be 0 < x < , then f is an invertible function. True False Range: −∞ < y < (d) If the domain of f ( x ) = ln ( e x ) is taken to be −∞ < x < , then f is an invertible function. True False Range: −∞ < y < 2. (6 points) A scientist discovers a dinosaur fossil which contains a certain amount of the radioac- tive isotope carbon-14. The amount of carbon-14, in micrograms, in the fossil can be modeled by c = 200 e kt , where t is the age of the fossil in thousands of years. (a) What was the original amount of carbon-14 in the fossil? 200 micrograms (b) What is the sign of k in the model? Why? negative, to give exponential decay. (c) If t = f ( c ) is the age of the fossil as a function of how many micrograms c of carbon-14 it currently contains, what type of function is f ( c )? Explain your answer. f ( c ) is a logarithmic function. Notice that the function c = f - 1 ( t ) is the amount of carbon as a function of time, which is an exponential function. An inverse of an exponential function is a logarithmic function.
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3 3. (8 points) For each graph, state the letter of the equation which best represents it.
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