The equation y=6.72(1.014)^x models the world population y, in billions of people, x-years after the year 2000. Find the year in which the world population is about 10 billion?

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Answer 1 · 2015-06-03T09:33:07

#y = 6.72*(1.014)^x#

#10 = 6.72*(1.014)^x#

#10/6.72 = 1.014^x#

#log(10/6.72) = log(1.014^x)#

#log(10/6.72) = x*log(1.014)#

#x = log(10/6.72)/log(1.014) = (log(10)-log(6.72))/log(1.014)#

#x = (log(10)-log(6.72))/log(1.014) =(1-log(6.72))/log(1.014) ~~ 28.59.#

So the world population would reach 10 billion in the middle of year #2028#. In fact it is expected to be around 2100.