I found this series of videos from a lecture by Albert Bartlett to be quite enlightening.

Exponential growth defined

YouTube - The Most IMPORTANT Video You'll Ever See (part 1 of 8)

(:youtube F-QA2rkpBSY:)

"The greatest shortcoming of the human race is our inability to understand the exponential function"

What is exponential growth?

Exponential growth is a mathematical function used to describe anything that is growing at a steady rate, e.g., your money in the bank earns a steady 5% per year (I wish). So the money is said to grow at a steady rate of 5% per year. Or in a fixed length of time it grows a fixed percentage.

Doubling time - time it takes to double starting point at steady rate. The formula for Doubling time...

Doubling time = 70 / % growth rate per unit time

Doubling time for 5% = 70 / 5 = 14

Why 70? Learn about natural logs

70 = 100 x (Natural log of 2) = 69.3

The natural logarithm, formerly known as the hyperbolic logarithm,[1] is the logarithm to the base e, where e is an irrational constant approximately equal to 2.718281828.

In simple terms, the natural logarithm of a number x is the power to which e would have to be raised to equal x

for example the natural log of e itself is 1 because e1 = e, while the natural logarithm of 1 would be 0, since e0 = 1. The natural logarithm can be defined for all positive real numbers x as the area under the curve y = 1/t from 1 to x, and can also be defined for non-zero complex numbers as explained below.

Growth of any doubling time is greater than all the growth that came before it!

70 year span (avg human life)

Exponential growth examples

YouTube - The Most IMPORTANT Video You'll Ever See (part 2 of 8)

(:youtube Pb3JI8F9LQQ:)

The Essential Exponential! - For the Future of Our Planet
by Albert A. Bartlett

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