How do I do all the math to come up with a final year in which there will be only one square meter for every person on earth?
"Given the current populations of 6,994,325,380 (as of 2/14/2012 at 10:49 am) as prvided by the U.S. Census bureau's web site, when will there be only one square meter for every person on earth?" I am taking glaciers and water into account.
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P = P_0 e^(rt) is the equation for population growth.
P_0 is the t=0 population (todays population in our problem)
e is Euler's number 2.718281828... it is on scientific calculators.
r is the population growth rate (0.015) the current rate.
t is the time in years.
The ln function, again on most calculators, is the inverse of the e^x function, it undoes e^x so ln(e^x) = x.
So solving for e^(rt) and then taking the ln of both sides of the above equation I get
ln(e^rt) = ln(P/P_0)
Since ln(e^x) = x we get
rt = ln(P/P_0)
t = (ln(P/P_0))/r
Since we know P, P_0, and r we can calculate the time it will take to reach that population on a calculator, which is what I did in my answer above.
Hope that helps.
I can give you a link that explains exponential population growth.
The surface area of the earth (including water and glaciers) is `510,072,000 km^2`
This is `510,072,000,000,000 m^2`
Assuming a 1.5% growth rate (world population grew 30% between 1990 and 2010).
Using `P=P_0 e^(rt)` for population growth.
`P_0 = 6,994,325,380`
`P = 510,072,000,000,000` we get
`e^(0.015t) = (510,072,000,000,000)/(6,994,325,380)`
Take the ln of both sides and divide by 0.015 to get
`t = ln((510,072,000,000,000)/(6,994,325,380))/0.015`
I get t = 746.480 years.
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