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Exam_fexam_3_ - MATH 140 THIRD EXAM Prof Pego November 8...

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Unformatted text preview: MATH 140 THIRD EXAM Prof. Pego November 8, 2002 Number your answer sheets from"1 to 4, and fill out all the information at the top of each sheet. Use one page per numbered problem. No calculators or computers are allowed. You must show all work to receive credit. Take care, and good luck. 1. (20 points) The half-life of the radioactive isotope strontium-90 is 29 years. The Chernobyl nuclear accident in 1986 released a lot of it into the environment. From each kilogram released, how much remains in 2002? (Your answer may contain unevaluated logarithms and exponentials.) 2. (20 points) A gardener wishes to enclose a rectangular garden with a brick wall along one side and wood fence along the other three sides. The brick wall will cost $80 per foot and the wood fence will cost $40 per foot. The garden should cover 600 square feet. What dimensions will minimize the total cost of wall and fence? (Note: Draw a figure and identify variables, describe what is desired, include domain, and justify Whether you obtain a maximum or minimum using lst or 2nd derivative tests.) 3. (40 points) Let (2x — 1)2 2x—1 3—4w 2x2 ’ ' x3 and f”(x)= x4 f(:c) 2 then f’(a7) = 4. (20 points) a. (10) Find a function h(t) such that h’(t) = ——32t+ v0 for all t, h(0) = 20 and h(1) = 0. (Here uo is a constant to be determined.) b. (10) If you use the Mean Value Theorem with f (m) = fl, what can you say that the expression V256 — V250 equals? Use your answer and the fact that V 256 = 16 to answer: 6 Is it true or false that V256 — V250 < 3—2 ? MW ...
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