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It is best represented as a logistic function because of the carrying capacity of the planet. The planet can only hold so many people before we run out of resources or space, so even if the same rate of increase happened for a 100 years, it may not stay exponential the whole time during the 100 years because of one of those factors that force us to stop increasing. The population will be forced to level out making it a logistic function.

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The world cannot simply keep growing exponentially.  The world will run out of resources for and space for human kind. With the increase of people it will also increase Carbon Dioxide emissions; thus, Global Warming will become a bigger prominent. The world is a logistic function because it cannot handle the harsh actions of so many people on this thing you call a planet.