In my world, a second space race pushes humanity farther than it has ever gone before. Humanity has carved up to moon between superpowers (the U.S. and China) and second rate space powers (E.U., Russia, India, Brazil, South Africa, etc.) with a combined population of 2.5 million, and has established on Mars, Ceres, Ganymede, and a blimp base on Venus.

The space race has also brought a storm of scientific advancement, including (albeit accidentally) the cure for old age, discovered while trying to find a cure for cancer, 75$ per kilo orbital launch using space hooks, "cheap" interplanetary travel using the moon, etc.

Eventually, Mars comes into the spotlight for exploitable deuterium deposits and natural resources, and tens of thousands of colonists follow suit. At the height of Mars' habitation, the perfect storm strikes the Earth, literally. A storm of solar flares knocks out 57% of the world's power grid. Hundreds of millions starve within a month, the world economy collapses overnight, anarchy ensues. Even worse, six months after the solar storm, a fungal epidemic breaks out like highly infective Botulism. It tears through the human population, turing cities and buildings into uninhabitable wastelands. Nobody can stop it.

At the end of this ordeal, 38% of the world's population is dead. Due to the nature of the disease, fungal spores linger in buildings where the diseased were, turning cities into disease vectors for decades. Technologically, humanity on Earth is in the gunpowder age. Politically, they are is in the dark ages. It will take centuries for man to recover.

Mars, now cut off from earth, still has an advanced industrial base, all of mankind's complete automation, a population of ~10,000, and all of mankind's technologically advancements - including biological immortality.

tl;dr Space age Earth got rekt, Mars got good, and now the Martians are stranded

My Question is

  • Given a birth rate of 44.2 per thousand people yearly, biological immortality, and a death rate of 5 per thousand people yearly, what will these martians population be after the 317 years it take for humanity to come back from the Apocalypse?

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    $\begingroup$ This is a lot of fluff wrapped around a math problem. It isn't a question about building a world. $\endgroup$ – sphennings Aug 30 '17 at 19:04
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    $\begingroup$ @sphennings It's called a joke, jeez. $\endgroup$ – user15036 Aug 30 '17 at 19:05
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    $\begingroup$ 38% die still leaves a population of several billion. The gunpowder dark ages couldn't come close to feeding this many people. Max is probably less than a billion. $\endgroup$ – Josh King Aug 30 '17 at 19:16
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    $\begingroup$ Net increase per year 0.0442 - 0.005 = 0.0392. In 317 years the population will increase by a factor of 1.0392³¹⁷ = 196619.6. Times 10000 that makes 1,966,195,811. Almost 2 billion people. You are welcome. -1. $\endgroup$ – AlexP Aug 30 '17 at 20:17
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    $\begingroup$ I do not think that your Earth scenario would work. A solar flare would trigger EMP, true. However, military and government equipment is hardened against it, so if you still have 40% of power grid working and militaries functioning Earth should not be facing social breakdown and anarchy. Military research facilities will stay functioning as well. So, considering that they discovered immortality, they should be able to take control of the fungal epidemic. Once a fungicide is developed disinfection of cities and buildings will be a matter of short time. $\endgroup$ – Olga Aug 30 '17 at 21:46

Population x (Birth rate - Death rate)^years

(44.2 - 5) /1000 + 1 = 1.0392

1.0392^317 = 196619.6

196619.6 * 10000 = 1.97 Billion People

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