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 on the chess board were used.

(a) How many grains of wheat did the hapless king contract to place on the 64th square? (Answer using scientific notation and round the decimal value to two decimal places.) grains of wheat

(b) There are about 1.1 million grains of wheat in a bushel. Assume that a bushel of wheat sells for $4.40. What was the value of the wheat on the 64th square? (Round your answer to the nearest ten thousand dollars.) $

Guest Mar 30, 2021

#1**+1 **

Grains = 2^{s-1} where s is the square number

so on day 1 2^{1-1} = 2^{0 }= 1 grain

on the 64^{th }square 2^{63} = 9.22 x 10^{18} grains

Value:

1.1 million = 1.1 x 10^{6}

^{ } 9.22x10^{18} / 1.1x106 * 4.4 = a lot of dollars is that price 4.40 dollars / bushel?

= 3689348815 x 10^{4} dollars

ElectricPavlov Mar 30, 2021