World population is now about 6 billion. The growth rate has been roughly 2% per year since the end of World War II (1945). If a 2% per year growth rate continued, how many years would it take for world population to reach 12 billion?
Answers (1)
This is not a physics question. It is a math question.
Suppose you start with population N and growth rate 2%. After one year your population is 1.02N. After two years your population is 1.02 x 1.02N = (1.02)^2 x N so the general equation after Y years is P = (1.02)^Y x N
Therefore 12 x 10^9 = (1.02)^Y x 6 x 10^9 Now rewrite.
(12x10^9)/(6 x 10^9) = (1.02)^Y
(1.02)^Y = 2 This is done with logarithms, which I have never used, so I can't give an exact answer. But it's a little under 36 years, using "rule of 72".
(1.02)^Y = 2
Y * log(1.02) = log(2)
Y = log(2) / log(1.02) = 35.002788...