### Decaying Dice Assignment

Added on - 21 Apr 2020

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Decaying dice1DECAYING DICEBy NameCourseInstructorInstitutionLocationDate

Decaying dice2DECAYING DICEModelling and exponential functionIntroductionThe decay of the radioactive nuclear is slow hence the rate of the decay can be determined atsome particular time. This is a result of the rate of the decay that is constant. Decay is a statistical process,this implies that there can be statistical analysis in determination of the rate of decay. Alternatively, thestatistical method can also be used to determine the number of times a given die can roll. Therefore, anexperiment is done to determine decay analogy of the radioactive nuclei. A die is thrown spontaneouslywhere the sides showing specific numbers are regarded as decayed for example, a specific number such asfive. The dice then are to be removed and counting is done to the remaining dice. Recording andrepresentation of the remaining die are done within a range of time. The remaining dice are thrown andthe recounting is also done. This process is done on and on until such a time when the number of dice thatdo not decay is reduced. A constant is used to represent the decay of the radioactive nuclei.in thisexperimentation, there is the assumption that dice have a single change in showing the specific numberhence this gives an equivalent of real decay of a radioactive decay, thus this constant is given as 1/6.

Decaying dice3Literature reviewMathematics of decay of the radioactive dice.with an assumption that one was to throw a dice at intervals of one hour and make counts on thesame.by throwing 500 dice simultaneously at the end of every hour is the easiest way of starting the test1.This implies that at the end of one-hour one-sixth of this dice will be removed and with perfect statisticsthen the remaining dice will be 416.66667.Generally, remaining number after that throw will be shown as;N1 = 500(1 − 1/6).When a throw is done for the second time we have;N2 = 500(1 − 1/6) (1 − 1/6) = 500(1−1/6)2General whilst when n number of mass is given as;Nn = 500(1 − 1/6) n.This is an indication that decay is a progressive geometry. The first twelve throws are the one that is usedin the determination of the dice that do not decay. This method is indicated in the table below and a graphplotted as the number of the remainingdie against the number of rolls asshown below.1Bennett, S. (2011).decaying of dice(2nd ed.). carlisle: Cengage Learning.Bennett, S. (2012).radioactive isotopes(2nd ed.). leicester: Cengage Learning,

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