After the first round only 32 teams will left.
After the second round 16 teams will left.
After the third round 8 teams will left.
After the fourth round only 4 teams will left.
After the fifth round only 3 teams will left.
After the sixth round only 1 team will left.
What is independent and dependent variable?
If x and y are two variables in an algebraic equation and every value of x is linked with any other value of y, then 'y' value is said to be a function of x value known as an independent variable, and 'y' value is known as a dependent variable.
What is an exponential function?
An exponential function is a mathematical function in the form f(x) = [tex]a^{x}[/tex] where x is a variable, and a is a constant called the base of the function.
According to the given question
We have an exponential function
[tex]f(x) = 64(\frac{1}{2} )^{x}[/tex]
And y-axis represents the teams remaining and x axis represents the tournaments round
Since, here the values of x are independent variables and values of y are dependent variables.
Now for the
Tournament round 1 ,
y = f(1) = [tex]64(\frac{1}{2} )=32[/tex]
⇒ 32 teams are remaining
Tournament round 2
[tex]y = f(2) = 64(\frac{1}{2}) ^{2}[/tex]
⇒ y = 16, only 16 teams are remaining
For round 3
[tex]y = f(3) = 64(\frac{1}{2}) ^{3} =8[/tex]
For round 4
[tex]y = f(4) = 64(\frac{1}{2} )^{4}= 4[/tex]
⇒ Only 4 teams are remaining
For round 5
[tex]y = f(5) = 64(\frac{1}{2} )^{5} = 2[/tex]
⇒ only 2 teams are remaining
For round 6
[tex]y = f(6) = 64(\frac{1}{2}) ^{6}=1[/tex]
⇒ only one team is remaining
By using these parameters we will plot a graph for tournament rounds .
Learn more about the exponential function here:
https://brainly.com/question/11487261
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