quiz9solutions - MAC1147: Quiz #9 11/3/2009 In the...

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Unformatted text preview: MAC1147: Quiz #9 11/3/2009 In the top-right corner of a clean sheet of paper, write your name, UFID, and section number. Please use a pen with blue or black ink. When you are nished, FOLD your paper in half lengthwise and write your name on the back. 1. For each of the following situations, state whether an exponential growth model, an exponential decay model, a logistic growth model, or a learning curve model is most appropriate to analyze the problem. (a) Francium-233 is one of the fastest decaying radioactive isotopes that occurs in nature, with a half-life of 22 minutes. Suppose you need to know how long it takes for a given sample to decay until there is only 10% remaining. Exponential decay model. (b) Suppose you have a particular strain of black mold which you think might be more virulent than other strains. To test this you want to measure how long it takes a few spores to develop into a colony in a petrie dish, and estimate how large the colony will eventually become. Logistic growth model. (c) In a cognitive development study, children are given a list of words, and then have to recall them an hour later. The same trial is repeated each day for a month; you are tracking the children's improvement over time and wish to nd the point at which further practice produces only negligible improvement. Learning curve model. 2. Suppose you order an 18-inch (diameter) pizza because you have friends coming over, but then your annoying roommate eats 240◦ of the pizza while you were cleaning the bathroom. To impress your friends you decide to compute the area of the pizza that your roommate ate. How much was eaten? 1 Area of a sector: A = 2 r2 θ, where θ is in radians. 240◦ = 43π radians, and r = 9. So π A = 1 (92 ) 43 = 54π in2 . 2 3. (BONUS) Draw the entire unit circle, with angles labeled in either degrees or radians, and coordinates labeled. A full unit circle is given in the textbook, after the index. 1 ...
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