a continuing increase of the population on Earth eventually encourages settlement of the moon and mars. After colonization of the moon and mars, births 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. Nonetheles, the rising earth population constantly relocates the moon and Mars depending on the relative differences in 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`1 = -3/2 (x1-x2) - (x1-x3) + 3/2 x1 x`2 = -1/2 (x2 -x1) - 1/2(x2 -x3) - x2 x`3 = -1/2 (x3 -x1) - 1/2 (x3 -x2) - 1/2x1 a) if at time t=0 there are five bilion people on earth , and no one on moon and mars, Whats the population distribution far in the future?
a continuing increase of the population on Earth eventually encourages settlement of the moon and mars. After colonization of the moon and mars, births 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. Nonetheles, the rising earth population constantly relocates the moon and Mars depending on the relative differences in 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`1 = -3/2 (x1-x2) - (x1-x3) + 3/2 x1
x`2 = -1/2 (x2 -x1) - 1/2(x2 -x3) - x2
x`3 = -1/2 (x3 -x1) - 1/2 (x3 -x2) - 1/2x1
a) if at time t=0 there are five bilion people on earth , and no one on moon and mars, Whats the population distribution far in the future?
b) suppose instead that at a time t=0, 5/3 bilion people were on the moon, leaving 10/3 bilion on earth, with Mrs as yet uncolonized. What s the population of distibution far in the future?
c) explain the relationship between the result in (a) and (b).
Step by step
Solved in 4 steps
