If the world population is estimated to be 7 billion in 2011, and is growing at a rate of 1.2%,when is the population likely to hit the 10 billion mark? a) 2140 b) 2041 c) 2195 d) 2184

2041

The given information tells you an exponential model can be written as ...

... y = 7·1.012^(x-2011)

where y is the population in billions and x is the year.

Filling in the question information and solving for x, we get ...

... 10 = 7·1.012^(x -2011)

... 10/7 = 1.012^(x -2011) . . . . . divide by 7

... log(10/7) = (x -2011)·log(1.012) . . . . take the log of both sides

... log(10/7)/log(1.012) = x -2011 . . . . divide by log(1.012)

... 2011 + log(10/7)/log(1.012) = x ≈ 2040.9 ≈ 2041

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