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We saw in Part 3.1 and Part 3.2 that world population does not seem to be growing exponentially. However, this growth might be modeled by a coalition differential equation of the form
and write it in the form
Show that P must satisfy
where C is an arbitrary constant.
How is T related to your constant of integration C?
This calculation shows that there is a finite time T at which the population P becomes infinite -- or would if the growth pattern continues to follow the coalition model.
It's clear that Doomsday hasn't happened yet. To assess the significance of the population problem, it's important to know whether the historical data predict a Doomsday in the distant future or in the near future. We take up that question in the next Part.
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