At a yearly basketball tournament, 84 different teams complete, after each round of the tournament, one-fourth of the team remain.

3 answers
Question:

At a yearly basketball tournament, 84 different teams complete, after each round of the tournament, one-fourth of the team remain.
Create a function which models the above scenario and explain how you arrived at each part of the function

Answers

84*(1/4)^x

Step-by-step explanation:

84 is the constant as it is the starting amount. However each round (x because the amount of rounds is constantly changing) divides the team by 4 or multiplies by 1/4 (Reciprocal).

So, if you wanted to see if the amount of teams after three rounds you would do:

84 * 1/4 * 1/4 * 1/4. However, any number times itself is an exponent, so we would simplify to 84³. But due to the fact we do not know how many rounds we are going to calculate we change the exponent to x.

a negative exponent is translated as follows:

[tex]a^{-m} = \dfrac{1}{a^m}[/tex]

so, we have

[tex]\left(5^{-1}+3^{-1}+2^{-1}\right)^{-1} = \left(\dfrac{1}{5}+\dfrac{1}{3}+\dfrac{1}{2}\right)^{-1} = \left(\dfrac{6+10+15}{30}\right)^{-1}=\left(\dfrac{31}{30}\right)^{-1}=\dfrac{30}{31}[/tex]

Y=-2x-6 is the answer

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