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

Guest Jan 24, 2018

#1**+3 **

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

hectictar
Jan 24, 2018

#1**+3 **

Best Answer

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

hectictar
Jan 24, 2018

#2**+2 **

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

ElectricPavlov
Jan 25, 2018