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