We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
138
1
avatar+33 

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+102995 
+1

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

43 Online Users

avatar
avatar
avatar