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.  

don't guess, because if you answer incorrectly, points are taken off. even if you don't finish, take your time. to study, use the sample questions. there is not much preparation to take the pre- tests.