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Unformatted text preview: M ATH 115 –F IRST M IDTERM October 7, 2008 NAME: INSTRUCTOR: SECTION NUMBER: 1. Do not open this exam until you are told to begin. 2. This exam has 10 pages including this cover. There are ?? 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. You are also allowed two sides of a 3 by 5 notecard. 7. If you use graphs or tables to obtain an answer, be certain to provide an explanation and sketch of the graph to show how you arrived at your solution. 8. Please turn off all cell phones and pagers and remove all headphones. PROBLEM POINTS SCORE 1 14 2 15 3 12 4 10 5 12 6 10 7 9 8 10 9 8 TOTAL 100 2 1. In 1999, a population of deer (a type of large animal) was set free on a previously uninhabited island in Lake Superior, in an attempt to establish a permanent population of deer on the island. The population of deer grew over time. Population measurements were made each year, as shown in the following table: Year 1999 2000 2001 2002 Population 20 23 27 31 Let P ( t ) be a function that gives the population of deer on the island as a function of time, t , measured in years since 1999 . (a) (2 points) In the context of this problem, give a practical interpretation for P (40) . (b) (2 points) In the context of this problem, give a practical interpretation for P − 1 (40). (c) (3 points) Assume that the deer population at time t is represented by an exponential func- tion P ( t ) = P a t . Find P and a , and express your answer as a function. (d) (2 points) According to your answer to part (c) what is the annual percent growth rate of the deer population? (e) (3 points) Use the table above to estimate ( P − 1 ) ′ (27) . Do not assume that the deer popula- tion is modeled by the formula from part (c)....
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