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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 

Guest Jan 24, 2018

Best Answer 

 #1
avatar+7164 
+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
avatar+7164 
+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
avatar+12566 
+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

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