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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.) $

 Mar 30, 2021
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Grains = 2s-1      where s is the square number 

   so on day 1      21-1 = 2= 1 grain

 

on the 64th  square    263 = 9.22 x 1018 grains

 

Value:       

1.1 million =     1.1 x 106

     9.22x1018 / 1.1x106    *   4.4     =   a lot of dollars        is that price   4.40 dollars / bushel?

                                                    = 3689348815 x 104   dollars

 Mar 30, 2021
edited by ElectricPavlov  Mar 30, 2021

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