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The athletics director at Peter’s school has created a message system that is used to notify team players in the event a game has to be canceled or rescheduled.  The message system is initiated when the director calls two captains. 

During the second stage of the message system, the captains each call two players. 

During the third stage of the message system, these players each call two other players. 

The message system continues until all players have been notified. 

If there are 50 players on the teams, how many stages will it take to notify all of the players?

 Feb 22, 2021
 #1
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This is an exponential function

 

\(2^x = 50\)

 

\(x = \log_2{50} = 5.643\)

 

It takes 5 stages to notify all the players.

 Feb 22, 2021
edited by CubeyThePenguin  Feb 22, 2021
 #2
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1st   stage      2 players notified

2nd stage       4 more players notified     total  6

3rd stage       8 more                               total  14

4th stage       16 more                             total 30

5th stage       32 more                             total > 50         5 stages needed

 Feb 22, 2021

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