Spring 2010 Final Solutions

Spring 2010 Final Solutions - Final Exam, STOR 112 Spring...

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Unformatted text preview: Final Exam, STOR 112 Spring 2010 Instructions: Work the problems in a blue book. You can write on the exam, but it will not be graded. Make sure your name and section number are on your blue book. (Section 1 = Pataki; Section 2 = Anderson). Clearly mark each problem number. Please answer the problems in order, and start each problem on a new page. (If you want to skip a problem, leave plenty of space for that problem.) You may use a calculator. All calculations should be done so that the final answer is accurate to four decimal places. When turning in your exam, please show your UNC OneCard to one of the in- structors. Please return the exam paper as well. Question 1. (10 points) Jada deposited P dollars in the bank 3 years ago. The bank has been paying interest at the rate of 5% per year, compounded daily (assume a 365 day year), and she now has $15,000 in the account. What is P ? Solution Denote the initial deposit by P . In 3 years, it grew to P 1 + . 05 365 3 365 = 15 , 000 dollars. Working out the expression on the left, we get 1 . 16182 P = 15 , 000 , i.e. P = 12 , 910 . 75 . So her initial deposit was approximately 12 , 910 . 75 dollars. Question 2. (30 points) The occupancy rate of the all-suite Wonderland Hotel, located near an amusement park is given by the function r ( t ) = 10 81 t 3- 10 3 t 2 + 200 9 t + 60 , where 0 t 12 , t is measured in months, t = 0 corresponds to the beginning of January. Management has estimated that the monthly profit (in thousands of dollars) is given as a function of the occupancy rate, r P ( r ) =- 3 5000 r 3 + 9 50 r 2 , where 0 r 100 , Find dP dt t =6 . 1 (it is not necessary to find an expression for dP dt in general). At what rate was the profit changing at the beginning of July? Make sure to state the units correctly. Solution We have dP dr =- 9 5000 r 2 + 18 50 r, and dr dt = 30 81 t 2- 20 3 t + 200 9 ....
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Spring 2010 Final Solutions - Final Exam, STOR 112 Spring...

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