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On a calendar, I put 1 grain of sand on May 1st, 2 grains of sand on May 2nd, 4 grains on May 3rd, and so forth, doubling the number of grains each day. On what day will I put down the 500th grain?

 Feb 15, 2019
 #1
avatar+98126 
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We can use the sum of a geometric series to solve this

 

Sum  =   First term  [ 1 - (common ratio)^n ] /  [ 1 - common ratio]

 

The common ratio is 2....and we are trying to find " n".....so we have

 

500 = 1 [ 1 - 2^n ] / [1  - 2 ]

 

500 = 1 [ 1 - 2^n ] / [ - 1 ]      multiply both sides by -1

 

- 500 =  1 - 2^n     subtract   1 from both sides

 

-500 - 1   =   -2^n       

 

-501 = - 2^n     multiply both sides by -1

 

2^n =  501      take the log of both sides

 

log 2^n = log 501    and we can write

 

n * log (2)  = log (501)        divide both sides by log (2)

 

n = log (501) / log (2) ≈  8.96 days 

 

 

cool cool cool

 Feb 15, 2019
edited by CPhill  Feb 15, 2019

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