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Final Exam - S09 - Name Math 10260 Final Exam May 6 2009...

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Name: Instructor: Math. 10260, Final Exam May 6, 2009 Be sure that you have all 16 pages of the test. Calculators are allowed for this examination. The exam lasts for two hours. The Honor Code is in effect for this examination, including keeping your answer sheet under cover. Sign the pledge. “As a member of the Notre Dame Community, I will not participate in or tolerate academic dishonesty”: Good Luck! PLEASE MARK YOUR ANSWERS WITH AN X, not a circle! 1. (a) (b) (c) (d) (e) 2. (a) (b) (c) (d) (e) ..................................................................... 3. (a) (b) (c) (d) (e) 4. (a) (b) (c) (d) (e) ..................................................................... 5. (a) (b) (c) (d) (e) 6. (a) (b) (c) (d) (e) ..................................................................... 7. (a) (b) (c) (d) (e) 8. (a) (b) (c) (d) (e) ..................................................................... 9. (a) (b) (c) (d) (e) 10. (a) (b) (c) (d) (e) ..................................................................... 11. (a) (b) (c) (d) (e) 12. (a) (b) (c) (d) (e) ..................................................................... 13. (a) (b) (c) (d) (e) 14. (a) (b) (c) (d) (e) ..................................................................... 15. (a) (b) (c) (d) (e) 16. (a) (b) (c) (d) (e) 17. (a) (b) (c) (d) (e) 18. (a) (b) (c) (d) (e) ..................................................................... 19. (a) (b) (c) (d) (e) 20. (a) (b) (c) (d) (e) ..................................................................... 21. (a) (b) (c) (d) (e) 22. (a) (b) (c) (d) (e) ..................................................................... 23. (a) (b) (c) (d) (e) 24. (a) (b) (c) (d) (e) ..................................................................... 25. (a) (b) (c) (d) (e) 26. (a) (b) (c) (d) (e) ..................................................................... 27. (a) (b) (c) (d) (e) 28. (a) (b) (c) (d) (e) ..................................................................... 29. (a) (b) (c) (d) (e) 30. (a) (b) (c) (d) (e) .....................................................................
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Multiple Choice 1. (5 pts.) The figure below displays the probability density function of a random variable X with values in the interval [0 , 4]. If the area above the interval [3 , 4] and below the graph of f ( x ) is equal to 0.2, then compute the integral R 3 0 f ( x ) dx. 1 x y 0 y = f(x) 2 3 4 0.2 (a) 1 (b) 0.8 (c) 0.6 (d) 0.4 (e) None of these. 2. (5 pts.) The figure above displays the probability density function of a random variable X with values in the interval [0 , 4]. Compute P (3 < X < 4). 2
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3. (5 pts.) For the supply curve displayed in the figure below, estimate the producer surplus by using Riemann Sums corresponding to Δ q = 2 and left-hand endpoints. Observe that the equilibrium quantity is 8 and the equilibrium price is 5. 4. (5 pts.) The demand curve of a certain item is p = D ( q ) = 81 q + 3 and its supply curve is given by p = S ( q ) = q + 3. Find the equilibrium price. 3
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5. (5 pts.) You have just borrowed $200,000 to buy a house at an annual interest rate of 5% compounded continuously. Suppose you can make payments at the steady rate of $18,000 per year. Use a differential equation and an initial condition to model the amount M ( t ) you will owe after t years. (Do NOT solve it!) (a) d M d t = 0 . 05 M - 18,000 , M (0) =200,000 (b) d M d t = - 0 . 05 M +18,000 , M (0) = - 200,000 (c) d M d t = 0 . 05 M +18,000 , M (0) =200,000 (d) d M d t = 0 . 05 M - 18,000 , M (0) = 0 (e) d M d t = 0 . 05 M - 18,000 , M (0) = 5,000 6. (5 pts.) Imagine that your company offers you the following two options: (I) For the next 10 years it deposits money continuously into an account A at a rate of S ( t ) =10,000 e 0 . 1 t dollars per year.
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