Question

At the end of each round of a basketball tournament, half of the teams are eliminated from the competition. If the tournament starts with 64 teams, which equation shows how many rounds, r, must be completed to have 2 teams left in the tournament?
A.2(1/2)^r=64
B.2(2)^r/2=64
C.64(1/2)^r=2
D.64(2)^r=1/2

Answer 1

you are looking at a GP
with a =32, and r = 1/2
term(n) = a r^(n-1)
2 = 64(1/2)^(n-1)
1/32 = (1/2)^(n-1)
(1/2)^5 = (1/2)^(n-1)
n-1 = 5
n = 6

illustration:
64, 32, 16, 8, 4, 2 , count them you will get 6

A is obviously wrong, r = -5 makes no sense
B gives us r = 10 , silly
C gives us r = 5, but my listing shows that we have 4 teams after 5 rounds
D is absurd, the left side of the equation is 2048 when r = 5

none of your equations are correct, should be
64(1/2)^(r-1) = 2

Answer 2

hhm idk this answer, anyone out there know??