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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

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  1. 16 May, 14:58
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    Answer

    B) 2041

    Explanation:

    The rate of growth per year is 1.2% which means after first year the population will be

    7 + 7 * (1.2/100)

    After second year

    7*1.012 + 7*1.012 (1.2/100)

    =7*1.012 (1+1.2/100)

    =7*1.012 (1.012)

    =7*1.012 * 1.012

    Similarly, after third year it will be as:

    =7*1.012 * 1.012 * 1.012

    So our after x year the growth will be

    7 (1.012) ^x

    We need to find, when the value will be 10 billion so our equation will be as:

    10=7 * (1.012) ^x

    We can solve it easily here.

    10/7 = (1.012) ^x

    Take log on both sides

    ㏒ 10/7 = ㏒ (1.012^x)

    ㏒ 10/7 = ㏒ (1.012^x)

    ㏒ 10/7 : ㏒ (1.012) = x

    x = 29.90 ≈ 30

    Conclusion:

    So it will take 30 years to take the world population to reach 10 billion if the rate of growth is 1.2%. Thus 2011 + 30 = 2041 is the correct answer.
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