There are a total of 128 teams at the start of a citywide 3-on-3 basketball tournament. Half the teams are eliminated after each round. Write and solve an exponential equation to determine after which round,x, there are 16 teams left.
The exponential equation is
There are 16 teams left after round
+9466 the number of teams after round 0 = 128
the number of teams after round 1 = (1/2) * 128
the number of teams after round 2 = (1/2) * (1/2) * 128
the number of teams after round x = (1/2)x * 128
(1/2)x * 128 = 16
Divide both sides of the equation by 128 .
(1/2)x = 1/8
We can express 1/8 as (1/2)3
(1/2)x = (1/2)3
So we can see that...
x = 3
+9466 the number of teams after round 0 = 128
the number of teams after round 1 = (1/2) * 128
the number of teams after round 2 = (1/2) * (1/2) * 128
the number of teams after round x = (1/2)x * 128
(1/2)x * 128 = 16
Divide both sides of the equation by 128 .
(1/2)x = 1/8
We can express 1/8 as (1/2)3
(1/2)x = (1/2)3
So we can see that...
x = 3
+36916 Similarly:
#teams left = 128/(2^x) where x = rounds
16 = 128/(2^x)
128/16 = 2 ^x
log (128/16) / log 2 = x x = 3 rounds
