Question

each year the local country club sponsors a tennis tournament. play starts with 128 participants. during each round, half of the players are eliminated.
write the rule: type your answer... i (use the ^ to do an exponent) (no commas)
how many participants remain after 4 rounds? type your answer...

Explanation:

Step1: Find the rule

The initial number of participants is \(a = 128\). The common ratio \(r=\frac{1}{2}\). The general formula for a geometric sequence is \(y = a\times r^{x}\), where \(x\) is the number of rounds. So the rule is \(y = 128\times(\frac{1}{2})^{x}\) or \(y=128\times2^{-x}\).

Step2: Calculate the number of participants after 4 rounds

Substitute \(x = 4\) into the formula \(y = 128\times(\frac{1}{2})^{x}\).

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Answer:

Rule: \(y = 128\times2^{-x}\)
Number of participants after 4 rounds: \(8\)