![globe-1290379_1280.jpg](https://steemitimages.com/DQmQsU5EKhRUkazGwHyoxzRxV5A65mi35Y6UqbEmWPcHrs8/globe-1290379_1280.jpg) ## "The greatest shortcoming of the human race is our inability to understand the exponential function"

-Albert Allen Bartlett

https://steemitimages.com/0x0/https://steemitimages.com/DQmevHD1ZLA5DKtPiMr25WAZvv5d9DUa9Xs4vpNrpzfNxLV/red-diamond.gif ### I'll explain... If you wish to find out the length of time a quantity takes to double, start by calculating the natural logarithm of 2, if you desire the time to triple use 3: ### ln(2) = 0.693 Multiply by 100 to work in percent: ### (ln2)100 = 69.3
Now you can take any steady growth rate and divide it into 70 to find out the doubling time: ### Doubling Time = 70/ 7% per year = 10 years
So, with a growth rate of only 7% the quantity doubles in 10 years. Not only that, the growth in that period will be greater than the total produced in all of preceding history. One of the presidents understood this principle: >In each of those decades (1950's and 1960's) more oil was consumed than in all of mankind's previous history.

-President Jimmy Carter

I highly recommend you check out Al Bartlett's great talk. It's a fantastic synthesis of math, politics and the environment. Please let me know your thoughts on population growth. To me it seems inevitable that a blight of some kind will cut back population. What that is, how and why it happens, I'd like to know! I'll leave you with a quote from one of the best science fiction writers of all time: >As you put more and more people into the world, the value of life not only declines, it disappears. It doesn't matter if someone dies, the more people there are, the less one individual matters.

-Isaac Asimov

https://steemitimages.com/0x0/https://steemitimages.com/DQmevHD1ZLA5DKtPiMr25WAZvv5d9DUa9Xs4vpNrpzfNxLV/red-diamond.gif ### References: [Arithmetic, Population and Energy (Lecture)](https://topdocumentaryfilms.com/arithmetic-population-and-energy-lecture/) [Al Bartlett's Website](http://www.albartlett.org/)