SOLUTION: If each of them tells 1 person, and then everybody tells exactly 1 other person, and so on, how long will it take until all 450 students in the school hear the rumor? Assume that t

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: If each of them tells 1 person, and then everybody tells exactly 1 other person, and so on, how long will it take until all 450 students in the school hear the rumor? Assume that t      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 1029066: If each of them tells 1 person, and then everybody tells exactly 1 other person, and so on, how long will it take until all 450 students in the school hear the rumor? Assume that the rate for telling the next person is 1 hour. That is, initially Jack and Jill know; after 1 hour, 2 more people know; after 2 hours, 2 more people know
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The total number of people after each hour is:
(0) +2%5E1+
(1) +2%5E1+%2B+2%5E2+
(2) +2%5E1+%2B+2%5E2+%2B+2%5E3+
(3) +2%5E1+%2B+2%5E2+%2B+2%5E3+%2B+2%5E4+
-----------------------
I notice that at hour number +n+,
the total that hear rumor is +2%5E%28+n+%2B+2+%29+-+2+
--------------
I can say:
+450+=+2%5E%28+n+%2B+2+%29+-+2+
+452+=+2%5E%28+n+%2B+2+%29+
+452+=+2%5En%2A2%5E2+
+452+=+4%2A2%5En+
+2%5En+=+113+
+n%2Alog%282%29+=+log%28113%29+
+.30103n+=+2.05308+
+n+=+6.8202+
+.8202%2A60+=+49.21+
All 450 students hear rumor after
6 hrs and 49 min
------------------
check:
+450+=+2%5E%28+n+%2B+2+%29+-+2+
+450+=+2%5E%28+6.8202+%2B+2+%29+-+2+
+450+=+2%5E8.8202+-+2+
+450+=+452.007+-+2+
+450+=+450.007+
error due to rounding off
You might want a 2nd opinion on this