Physic homework. urgent help due tomorrow

Question

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?

Answer 1

A growth rate of 2% per year means that at the end of a year, the population is 1.02 times what it was at the beginning of the year.  Keep this up for n years and you end up with

 

P(n) = P₀(1.02)ⁿ,

 

where n is the number of years elapsed since the population was P₀.  Assuming that at this time P₀ is 6 billion, we can get the number of years it takes to reach 12 billion from

 

12 billion = (6 billion) (1.02)ⁿ

 

2 = 1.02ⁿ

 

log2 = n log1.02

 

n = log2 / log1.02 ≅ 35.00

 

It will take about 35 years to reach 12 billion, starting with 6 billion at the present, at a growth rate of 2% per year.

 

(By the way, this is not really a physics problem.)

Answer 2

The equation to solve this problem is 6 x 10^9(1.02)^n=future population

n=number of years.

 

Now to find the year where the population will be 6x10^9(1.02)^n=12 x 10^9

1.02^n=12x10^9/6x10^9=2

nLog1.02=log2

n=log2/log1.02

n=35 years from today or 2052