SOLUTION: can you please help me solve this problem?! In a large city league, the boys' baseball teams hold a tournament. If there are 40 teams in the league and half of the teams are e

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Question 188787: can you please help me solve this problem?!

In a large city league, the boys' baseball teams hold a tournament. If there are 40 teams in the league and half of the teams are eliminated in each round of games, how many teams are left after 3 rounds?
a. +40%281.05%29%5E3+
b. +40%28.05%29%5E3
c. +40%28.5%29%5E3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: the fraction 1%2F2 is equivalent to the decimal number 0.5


After one round, you simply take half of the original 40 to get


40%280.5%29=20


Now after the second round, you then take half of the remaining teams (which is 20) to get

20%280.5%29=10


Note: this is the same as saying 40%280.5%29%280.5%29


Finally, after 3 rounds, take half of the 10 leftover to get


10%280.5%29=5

Note: this is the same as saying 40%280.5%29%280.5%29%280.5%29


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Notice how after each round we're multiplying each result by 0.5.


So after "n" rounds (where "n" is a positive number), there are


40%280.5%29%5En teams left


Remember, exponentiation is simply shorthand notation for repeated multiplication.


Now plug in n=3 to get


40%280.5%29%5E3


So after 3 rounds, there are 40%280.5%29%5E3 teams left. This means that the answer is C)


Take note how 40%280.5%29%5E3=5 (which is the number of teams that we found earlier)