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140Bquiz11a

# 140Bquiz11a - 1 MATH 140B QUIZ#11 Date Dec 3 2007 2 1 A...

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1 MATH 140B QUIZ#11 Date: Dec 3, 2007 [ 2 ] 1. A population of pheasants is introduced on an island. Lacking any natural predators, the population flourished to 560 three years later. Assume that the population grows according to the Malthusian model for population growth. That is, if P ( t ) denote the population at time t , and P 0 is the intial population, then dP dt = k · P P (0) = P 0 . where k is a positive constant of proportionality. Find the value of k, and use it to determine the generation (doubling) time in years. Round your answer to the nearest decimal. A) 1 B) 1.2 C) 1.4 D) 1.6 E) None of the above [ 2 ] 2. The Beer-Lambert Law says that the intensity, I ( x ) , of light at depth x meters in seawater is given by the decaying exponential function I ( x ) = I 0 · a x where 0 < a < 1 is a constant, and I 0 is the intensity of light at the surface. The photic zone is the depth where the intensity of light is 1% of what is it at the surface. In Cape Cod, MA the photic zone occurs at 16 meters. Find the value of the base a.

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