## "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: Sn = [a(1 - rn)]/(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 * 1019
Therefore the entire board would weigh a whopping 6 * 1014 kg!
The ratio of this weight to the entire human population on the year 2000 would be:

mass of wheat/mass of population2000

(6 * 1014 kg)/(6 * 109 * 72 kg) = 1400 : 1!

That is the board would outweigh the earth's human population about 14 hundred times!