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# 6.5 Algebra 1

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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

Jan 24, 2018

#1
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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

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
#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

Jan 25, 2018