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\lhead{Team \# 2008005}
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Letter to George R.R.
 Martin
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Dear Martin,
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We are a group taking part in the competition of MCM, and we also fascinate
 the TV series
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Game of Throne
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s, which is adapted from your famous novel
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A Song of Ice and Fire
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.
 We are especially interested in the three dragons appearing in your novel.
 Dragon is a mysterious and formidable creature, which raises our curiosity
 for deeply research.
 We present our findings in this letter, hoping these will be helpful for
 your writing.
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We take the biggest dragon Balerion, the Black Dread, as an example.
 According to the description in your novel, Balerion's head is as large
 as a carriage.
 We use the body of T.
 rex to analogize, estimating that the mature Barlerion's weight will be
 281.6 tons.
 By referring to the biological law, we determine that it takes 280 years
 for Barlerion to reach its upper limit weight.
 Its growing curve can be depicted as 'S' trend.
 The dragon is in the initial growth stage before the age of 19.
 After the age of 131, the dragon enters the steady growth stage.
 The exponential growth stage comes from age 19 till 131.
 The dragon grows fastest at the age of 52.
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For the total energy expenditure for a dragon, we do not consider the case
 with magic, which means the dragon cannot create energy by itself.
 The total energy expenditure for the dragon can be divided into five parts:
 the energy for the basic metabolism, growth, flying, breathing fire and
 recovery from trauma.
 We suppose that the dragon will fly and breath fire only while it is predating,
 and the time interval for its predation lasts for two days.
 It will consume almost 140 billion calories.
 This means the dragon has to eat 178 sheep and 470 cattle per two days,
 which is tremendous.
 The total energy expenditure for dragon mostly consists of the energy for
 basic metabolism in its whole life.
 The energy for breathing fire first takes a high percentage of total energy
 expenditure when the dragon is young, and then decreases until become steady.
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Besides, if the dragon exists in real life, this will obviously bring a
 great impact on the environment.
 We consider a situation of an area including three preys: sheep, cattle,
 and hare, which differs a lot in distribution density and meat energy.
 Then we stimulate the condition within the time interval for a two days'
 predation.
 As a result, cattle are most affected, followed by sheep, and hares take
 the least.
 That is to say, the dragon has a great impact on the prey with high energy
 and dense distribution, and has little impact on prey with low energy and
 sparse distribution.

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Then, our model considers that dragons might travel to different regions
 of the world under different climates.
 The climate changes will both influence the dragon and the preys' distribution.
 We choose four states in Australia to simulate, of which the temperature
 and humidity are different.
 Our results show that the higher the temperature, the less energy the dragon
 consumes.
 The higher the humidity, the lower the energy the dragon needs.
 And the influence of temperature on the dragon is greater than humidity.
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Besides, if we suppose the dragons breed through sexual multiplication,
 it will not be stable for three dragons to make up of a population.
 According to scientific researches, we discover that the number of individuals
 which consists of a stable population will be more than 500.
 After modeling, we find it will take approximately 2.33
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10
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 km
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 area for these dragons to live, almost 30% of Australia.
 In summary, it is possible for the dragon to be alive on the earth theoreticall
y, but require a lot of resources and territory.
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Yours sincerely,
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Team 2008005
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