The number of teams y remaining in a single elimination tournament can be found using the exponential function y = 128 (frac{1}{2})^x , where x is the

ruigE

ruigE

Answered question

2021-02-16

The number of teams y remaining in a single elimination tournament can be found using the exponential function y=128(12)x , where x is the number of rounds played in the tournament.

a. Determine whether the function represents exponential growth or decay. Explain.

b. What does 128 represent in the function?

c. What percent of the teams are eliminated after each round? Explain how you know.

d. Graph the function. What is a reasonable domain and range for the function? Explain.

Answer & Explanation

joshyoung05M

joshyoung05M

Skilled2021-02-17Added 97 answers

(a) For an exponential function in the form y=abx, If b>1, the function is increasing and is an exponential growth function. If 0<b<1, the function is decreasing and is an exponential decay function. Because b=12<1, then the function represents an exponential decay.

(b) In an exponential function y=abx, a represents the initial value so 128 means that there were initially 128 teams in the tournament.

(c) The exponential decay function is given by: A(t)=a(1r)t where a is the initial amount, (1r) is the decay factor, and r is the rate of decay. Using the value of b,b=1r12=112 So, the rate of decay is: r=12=0.5or50% This means that 50% of the teams are eliminated after each round.

(d) Both the round numbers and the number of teams must be positive integer values and 1 winner is determined after 7 rounds. Hence, a reasonable domain is the integer values from 0 to 7. A reasonable range is from 1 to 128.

madeleinejames20

madeleinejames20

Skilled2021-06-11Added 165 answers

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