### 7.2 Exponential Patterns

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• Math Help

Here are some general observations about the graph in Example 5.

• The graph is increasing from left to right.
• The point of maximum growth occurs at one-half of the maximum sustainable population.
• Before reaching the point of maximum growth, the growth rate is increasing.
• After reaching the point of maximum growth, the growth rate is decreasing.

• Consumer Suggestion

Did you know that Thomas Malthus is responsible for popularizing the economic theory of rent?

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• Checkpoint Solution

I think it's possible that Malthus' prediction will come true--that population will grow exponentially until a permanent poor class is created due to lack of resources--but I don't think it's inevitable. Many developed countries have declining fertility rates, and the percentage of people living in poverty has decreased recently throughout the world. Many predict the world population will level off around the year 2050. It's also possible that Malthus underestimated the ability of science to create new means of subsistence. Great advancements in agricultural efficiency have been made since his time, and scientists are currently working on lab-grown meat. I also think that through improved awareness of the population problem and better education and access to birth control, even areas where population growth is the highest and poverty is the worst, like Sub-Saharan Africa, could improve before a Malthusian catastrophe happens.

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```__    __     ___      ____       ___     _    _
\ \\ / //   / _ \\   |  _ \\    / _ \\  | || | ||
\ \/ //   / //\ \\  | |_| ||  / //\ \\ | || | ||
\  //   |  ___  || | .  //  |  ___  ||| \\_/ ||
\//    |_||  |_|| |_|\_\\  |_||  |_|| \____//
`     `-`   `-`  `-` --`  `-`   `-`   `---`

```