SOLUTION: a person got to know about a message, within 5 minutes he informed it to another 2 persons similarly each person who got to know about the message informed it to another 2 persons

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Question 1068436: a person got to know about a message, within 5 minutes he informed it to another 2 persons similarly each person who got to know about the message informed it to another 2 persons. At 10.30 Am 729 people got to know about the message.at what time 1st person got to knew about the message?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If I read this right, every 5 minutes, the number
of people who get the message doubles.
At start time +t+ , +1+ person
+t+%2B+5+, +1+%2B+2%5E1+=+3+
+t+%2B+10+, +1+%2B+2%5E1+%2B+2%5E2+=+7+
+t+%2B+15+, +1+%2B+2%5E1+%2B+2%5E2+%2B+2%5E3+=+15+
+t+%2B+20+, +1+%2B+2%5E1+%2B+2%5E2+%2B+2%5E3+%2B+2%5E4+=+31+
It looks like, if +n+ is the number of 5 minute
intervals, then the number of people with the
message is +2%5E%28+n%2B1+%29+-+1+
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At 10:30 +729+ people got the message
+2%5E%28+n+%2B+1+%29+-+1+=+729+
+2%5E%28+n%2B1+%29+=+730+
+%28+n%2B1+%29%2Alog%282%29++=+log%28+729+%29+
+.30103%2A%28+n%2B1+%29+=+2.86273+
+n+%2B+1+=+2.86273%2F.30103+
+n+%2B+1+=+9.50977+
+n+=+8.50977+
and
+8.50977%2A5+=+42.5489+ minutes
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10:30 minus +30+ min is 10:00
That leaves +12.5489+ min
+60+-+12.5489+=+47.4511+
also: +.4511%2A60+=+27+
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The 1st person know the message at 9:47:27
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DEFINITELY get another opinion on this.
I'm pretty much winging it here