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

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.