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Unformatted text preview: Name : Section : UFID: Show all of your work to receive credit. 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. MAC1140, Quiz 17 1. A chemist is analyzing a 1000g sample of a radioactive substance. She nds that after 2 hours, 250g of the substance remains, while the rest has decayed into other elements. (a) Find a and b in the exponential decay model y = ae-bt to describe this situation as a function of time (hint: nd the half-life rst) (b) How long will it take until there is only 100g of substance left? 2. A microbiologist is testing how dierent environments aect the growth of a strain of bacteria. There will be 1000 bacteria initially. From previous experiments, He expects the bacteria to reach 2000 in number after one hour, and to eventually reach 11,000 in number. He wants to set up a logistic growth model, but all he remembers from MAC1140 is that a logistic growth model follows the form a , where y will represent the amount of bacteria. y= -rt
1 + be (a) What is a in the model? (Hint: what happens to e-rt as t gets bigger?) (b) What is b in the model? (Hint: use the initial amount of bacteria, when t = 0) (c) What is r in the model? (Hint: what is y when t = 1?) ...
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