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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 800g sample of a radioactive substance. She nds that after 2 hours, 200g 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 80g of substance left? 2. A microbiologist is testing how dierent environments aect the growth of a strain of bacteria. There will be 500 bacteria initially. From previous experiments, He expects the bacteria to reach 1000 in number after one hour, and to eventually reach 5,500 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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