8. Physical model: radioactive decay series of iodine-133 → xenon-133 → cesium-133. A seriesof equations that can be used to describe the concentrations of two radioactive elements a(iodine-133, which decays into xenon-133) and y (xenon-133, which is created by the decayof iodine-133 and decays into cesium-133) is given by:drdtdy= A1x – A2ydtwhere A1 and A2 are positive constants. Find a solution for r(t) and y(t) subject to the initialconditions #(t = 0) = xo and y(t = 0) = y0-

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Answered: 8. Physical model: radioactive decay…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 45E: Epidemic Model In a population of 200,000 people, 40,000 are infected with a virus. After a person...

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Epidemic Model In a population of 200,000 people, 40,000 are infected with a virus. After a person becomes infected and then recovers, the person is immune cannot become infected again. Of the people who are infected, 5 will die each year and the other will recover. Of the people who have never been infected, 25 will become infected each year. How many people will be infected in 4 years?
In Alpha Decay: 1 atomic number decreases by 4 and mass number decreases by 4 2 atomic number and mass number are unchanged 3 atomic number decreases by 4 and mass number decreases by 2 4 atomic number decreases by 2 and mass number decreases by 4
2) Two strains of bacteria are growing in seperate petri dishes. Intitially, there are strain A 300 bacteria and, from a prior experiment, you know that the population should double every 20 minutes. Having never worked with strain B before, you monitor its growth over the first hour and notice that there are 200 bacteria after 30 minutes and 600 bacteria after 1 hour. a) Let t be the number of hours that have passed since the two populations of bacteria start growing. Express the number of strain A bacteria as a function of t. (Your answer should be of the form PA (t) = Ca bt for some numbers C, a and b.) b) Express the number of strain B bacteria as a function of t, (Again, your answer should be of the form P B (t) = Cabt for some numbers C, a and b, possibly different that those you found in (a)).) c) How many strain B bacteria were there intitially?
2. Factory A produces a solution of 40% concentration of chemical Y at a rate of 7 kg/min, while factory B produces a solution of 20% concentration of chemical Y at a rate of 4 kg/min. Both solutions are fed into a mixer containing 60 kg of a 25% concentration solution of chemical Y. The mixture leaves the mixer at a rate of 10 kg/min. Assuming uniform mixing, what will be the concentration of chemical Y in the final solution after 20 minutes?2)

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