**On this page...** (hide)

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

## Exponential growth defined

(: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 Pb3JI8F9LQQ:)

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