Pre-Calculus Practice Problem 111

# Pre-Calculus Practice Problem 111 - t ≈ 9.2 hours 3 A...

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Unit 3, Activity 8, Applications Involving Exponential Growth and Decay with Answers Blackline Masters, Advanced Math-Pre-Calculus Page 109 Comprehensive Curriculum, Revised 2008 1. The number of radioactive atoms N of a particular material present at time t years may be written in the form N = 5000e - kt , where 5000 is the number of atoms present when t = 0, and k is a positive constant. It is found that N = 2500 when t = 5 years. a) Determine the value of k . k = .1386 b) At what value of t will N = 50? t 33.3 years 2. A cup of coffee contains about 100 mg of caffeine. The half-life of caffeine in the body is about 4 hours which means that the level of caffeine in the body is decaying at the rate of about 16% per hour. a) Write a formula for the level of caffeine in the body as a function of the number of hours since the coffee was drunk. A = 100(.84) t b) How long will it take until the level of caffeine reaches 20 mg?
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Unformatted text preview: t ≈ 9.2 hours 3. A radioactive substance has a half-life of 8 years. a) If 200 grams are present initially, how much will remain at the end of 12 years? A ≈ 70.7grams b) How long will it be until only 10% of the original amount remains? b) t ≈ 26.6 years 4. The Angus Company has a manufacturing process that produces a radioactive waste byproduct with a half-life of twenty years. a) How long must the waste be stored safely to allow it to decay to one-quarter of its original mass? 40 years b) How long will it take to decay to 10% of its original mass? 66.4 years c) How long will it take to decay to 1% of its original mass? 132.9 years 5. A bacteria population triples every 5 days. The population is P o bacteria. a) Write an equation that reflects this statement. ( ) 5 3 t o P P = b) If the initial population is 120, what is the population i) after 5 days 360 ii) after 2 weeks 2600...
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