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.