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# Tuff word problem:C

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In 1969, in a report entitled Resources and Man, the U.S. National Academy of Sciences concluded that a world population of 10 billion “is close to (if not above) the maximum that an intensely managed world might hope to support with some degree of comfort and individual choice.” For this reason, 10 billion is called the carrying capacity of Earth. In 1999, the world population reached 6 billion and in 2011 the world population reached 7 billion. If exponential growth continues at this rate, in what year will Earth’s carrying capacity be reached?

Jun 6, 2018

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2011 - 1999 =12 years - when the population increased by 1 billion people.

[7 / 6]^(1/12) =1.01292 - 1 x 100 = 1.292% compounded annual growth in population.

Future Population =7 x (1.01292)^n, where n= number of years after 2011

10 = 7 x (1.01292)^n, solve for n

10/7 = (1.01292)^n     take the log of both sides

n =Log(10/7) / Log(1.01292)

n = 27.784 = ~ 28 years after 2011 - when the world's population will reach 10 billion people. Or:

2011 + 28 =2039 AD.

Jun 6, 2018