**"The Power of Exponential Growth"**

*by* Mike Grayson

Suppose you have a checkerboard and on the first square of that board
you placed a single grain of wheat. Then suppose you doubled the grain of
wheat with the next square, and the next, and so on until you reached the
last one -- the 64th square (in case you've forgotten). Now how much would
the entire mass of the board weigh?

### Here are some facts needed to find the solution:

- A typical grain of wheat weighs about 3.25 * 10
^{-5} kg
see the
AWB home page.
- Geometric sum formula: S
_{n} = [a(1 - r^{n})]/(1 - r)

Where r is the rate of doubling, a = 1 is the initial number in the
series, and n = 64 is the number of doubling periods.

If one applies the geometric sum formula we find that the total
number of grains = 1.844674407 * 10^{19}

Therefore the entire
board would weigh a whopping 6 * 10^{14} kg!

The ratio of
this weight to the entire human population on the year 2000 would be:

mass of wheat/mass of population_{2000}

(6 * 10^{14} kg)/(6 * 10^{9} * 72 kg) = 1400 : 1!
That is the board would outweigh the earth's human population about
14 hundred times!

*Last update: April 21, 1999*