Chapter 4.1, Problem 15E

Reminder Round all answers to two decimal places unless otherwise indicated.

Grains of Wheat on a Chess Board A children’s fairy tale tells of a clever elf who extracted from a king the promise to give him one grain of wheat on a chess board square today, two grains on an adjacent square tomorrow, four grains on an adjacent square the next day, and so on, doubling the number of grains each day until all 64 squares of the chess board were used. How many grains of wheat did the hapless king contract to place on the $64\text{th}$ square? There are about $1.1\text{million}$ grains of wheat in a bushel. Assume that a bushel of wheat sells for $\$4.25$. What was the value of the wheat on the $64\text{th}$ square?