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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