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### 140Bquiz11a

Course: MATH 140B, Fall 2007
School: Penn State
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Word Count: 405

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140B QUIZ#11 Date: 1 MATH 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 P0 is the intial population, then dP =kP dt P (0) = P . 0 where k is a positive...

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140B QUIZ#11 Date: 1 MATH 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 P0 is the intial population, then dP =kP dt 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) B) C) D) E) 1 1.2 1.4 1.6 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) = I0 ax where 0 < a < 1 is a constant, and I0 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. A) B) C) D) E) 1/4 1/3 1/2 3/4 4/5 [ 2 ] 3. Iodine-125 is often used to treat cancer and has a half-life of 60.1 days. Suppose that a sample Iodine-125 of decreased by 25% while in storage. How long was the sample sitting on the shelf? Round your answer to the nearest number of days. A) B) C) D) E) 25 30 35 40 None of the above 2 [ 2 ] 4. A body is discovered in the basement of a building. The constant room temperature is 70 F, and the body temperature is initially 85 F. One hour later, the body temperature is 80 F. How many hours before the body was discovered did the time of death occur? A) B) C) D) E) 1.0 1.3 1.6 1.9 None of the above [ 2 ] 5. Radioactive Strontium-90 has a half-life of 29 years and is potentially very dangerous to man. If deposited into pasture by acid rain, it will eventually make its way into plants and into cows milk. About 3% of the strontium 90 entering the human body becomes a permanent part of bone tissue, where its radioactivity could cause cancer. If it has been determined that the strontium-90 level in the pasture is 3 times the safe level, then how many years will it take before the pasture can again be used for grazing? Approximate to the nearest whole number of years. [Hint: you do not use the value 3% in the solution]. A) B) C) D) E) 30 38 42 46 None of the above
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