3. A continuing increase of the population on Earth eventually encourages settlement of the moon and of Mars. After colonization of the moon and Mars, birth rates continue to exceed death rates on Earth, but life is hard away from Earth so that the opposite is true elsewhere in the solar system. Nonetheless, the rising Earth population constantly relocates to the moon and Mars depending on the relative differences in the population sizes. You have modelled the population dynamics via the following differential equations, where x1(t) is the Earth population at time t, x2(t) is the Moon population, a and x3(t) is the population on Mars. 3 (x1 - x2) – (X1 – X3) +X1 x' = xị = -(x2 - x1) -X2 - x3) – x2 (X3 (x3 - X2) = -

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3. A continuing increase of the population on Earth eventually encourages settlement of
the moon and of Mars. After colonization of the moon and Mars, birth rates continue to
exceed death rates on Earth, but life is hard away from Earth so that the opposite is
true elsewhere in the solar system. Nonetheless, the rising Earth population constantly
relocates to the moon and Mars depending on the relative differences in the population
sizes. You have modelled the population dynamics via the following differential
equations, where x1(t) is the Earth population at time t, x2(t) is the Moon population, a
and x3(t) is the population on Mars.
x' =-(서-X2)-(xi - Xs) + 극제
x = -x2 - x,) -(x2 - x3) - X2
(x3 - x,) -(x3 - x,) -
:(X2
X1
= -
mIN HIN 1N
Transcribed Image Text:3. A continuing increase of the population on Earth eventually encourages settlement of the moon and of Mars. After colonization of the moon and Mars, birth rates continue to exceed death rates on Earth, but life is hard away from Earth so that the opposite is true elsewhere in the solar system. Nonetheless, the rising Earth population constantly relocates to the moon and Mars depending on the relative differences in the population sizes. You have modelled the population dynamics via the following differential equations, where x1(t) is the Earth population at time t, x2(t) is the Moon population, a and x3(t) is the population on Mars. x' =-(서-X2)-(xi - Xs) + 극제 x = -x2 - x,) -(x2 - x3) - X2 (x3 - x,) -(x3 - x,) - :(X2 X1 = - mIN HIN 1N
a. If at time t = 0 there are five billion people on Earth, and no one on Moon and Mars,
what is the population distribution far in the future?
b. Suppose instead that at time t = 0,5/3 billion people were on the Moon, leaving
10/3 billion on Earth, with Mars as yet uncolonized. What is the population
distribution far in the future?
c. Explain the relationship between the result in (a) and (b).
Transcribed Image Text:a. If at time t = 0 there are five billion people on Earth, and no one on Moon and Mars, what is the population distribution far in the future? b. Suppose instead that at time t = 0,5/3 billion people were on the Moon, leaving 10/3 billion on Earth, with Mars as yet uncolonized. What is the population distribution far in the future? c. Explain the relationship between the result in (a) and (b).
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