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Math Portfolio: Radioactive Decay

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Introduction

Math Portfolio 2 Radioactive Decay Lee, Grade 11 This portfolio is about exponential decay (radioactive decay). Exponential decay means there's a decrease at a rate proportional to its value. In this case, it talks about a community with an initial population of 100, and each member of the community has the potion of living in 1 of 8 places with equal probability. We are assigned to display the random number of allocation, make tables and graphs accordingly, choose an appropriate model, and list some errors and limitations. Year 0 1,2,1,8,8,4,3,3,7,3,2,4,3,8,2,2,2,6,5,4,8,3,5,2,5,6,6,5,2,15,7,2,5,8,6,1,5,6,2,5,2,6,7,1,3,8,1,6,7,4,7,7,8,3,4,8,6,5,58,3,3,2,7,6,3,3,7,5,5,7,5,6,3,5,8,2,2,8,1,7,7,7,6,4,6,3,7,84,1,4,3,3,3,6,8,1,2 Location Frequency of Population 1 9 2 14 3 16 4 8 5 14 6 13 7 13 8 13 RandInt (1,8) Result: 8 Location 8 Eliminated Total population= 100-13=87 Year 1 1,5,8,4,4,6,7,5,2,1,7,4,1,5,1,7,6,3,4,8,8,7,7,8,5,8,5,4,7,2,8,4,1,3,5,1,3,7,4,8,2,4,1,1,5,7,1,7,1,2,3,2,4,4,6,6,8,3,4,5,4,7,3,1,6,7,2,4,1,2,6,1,5,7,7,7,5,6,6,6,4,5,5,7,6,1,3 Location Frequency of population 1 14 2 7 3 7 4 14 5 12 6 9 7 16 8 8 RandInt (1,8) Result: 5 Location 5 eliminated 87-12=75 Year 2 6,7,2,6,6,1,5,7,1,8,5,4,4,5,8,2,5,7,4,5,3,3,2,7,6,6,1,2,3,3,3,7,1,3,3,6,3,6,5,2,4,5,5,2,2,3,1,8,5,6,3,8,6,5,5,8,2,7,3,1,4,4,7,5,8,1 Location Frequency of population 1 7 2 9 3 17 4 6 5 13 6 10 7 7 8 6 RandInt(1,8) ...read more.

Middle

Result: 6 31-6=25 Year 9 3,6,6,2,2,2,7,1,4,7,7,8,4,2,5,1,6,2,1,4,5,2,1,2,2 Location Frequency of population 1 4 2 8 3 1 4 3 5 2 6 3 7 3 8 1 RandInt (1,8) Result: 8 25-1=24 Year 10 6,8,5,1,6,7,2,8,4,1,8,7,5,8,2,5,7,8,7,4,7,4,3,2 Location Frequency of population 1 2 2 3 3 1 4 3 5 3 6 2 7 5 8 5 RandInt(1,8) Result: 7 24-5=19 Year 11 5,4,2,1,3,3,7,2,8,4,5,6,1,2,6,5,6,6,4 Location Frequency of population 1 2 2 3 3 2 4 3 5 3 6 4 7 1 8 1 RandInt(1,8) Result: 8 19-1=18 Year 12 3,7,8,4,7,4,1,2,7,1,3,6,3,8,1,6,3,8 Location Frequency of population 1 3 2 1 3 4 4 2 5 0 6 2 7 3 8 4 RandInt(1,8) Result: 1 18-3=15 Year 13 7,4,5,8,7,5,7,3,4,4,7,3,3,4,1 Location Frequency of population 1 1 2 0 3 3 4 4 5 2 6 0 7 4 8 1 RandInt(1,8) Result: 5 15-2=13 Year 14 1,4,3,3,3,1,5,4,3,8,6,7,3 Location Frequency of population 1 2 2 0 3 5 4 2 5 1 6 1 7 1 8 1 RandInt(1,8) ...read more.

Conclusion

The limitations will be: 1) In this case, we assume that once the place is cleared, the will be other animals occupying the space. But when animals feel there is a danger, they won't settle there. 2) We use RANDOM NUMBERS, which allows us to reuse the number that we used already in the data. This might give less accurate results. 3) We can see no Growth. Is it possible only to have decaying process without any growth? 4) The attack of predators which in this case happens annually, but in the real world the animals may attack more than once a year. Q3) The concept: The concept is limited to decay without growth. The assumptions made will be 1) The population has no other option that those 8 places provided 2) Members are not going out from that 8 location 3) There's no regular predator attack. The limitations will be more or less similar to the limitations of the previous model. With these calculations and graphs, we have proven that the random allocation of population and it's predator's attack results in half life graph ( exponentially decaying graph) ...read more.

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