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Answer :
Final answer:
The equation that best models the number of players remaining after each round in the tennis tournament is y = 128(0.5)^x. The situation represents an exponential decay, halving the number of players in each subsequent round, so Option 3 is the correct choice.
Explanation:
The student is asking for the equation that best models the number of players remaining after each round in a tennis tournament that starts with 128 players. The number of players halves with every round, which suggests an exponential decay model for the situation. Mathematically, exponential decay is represented by the formula y = a(0.5)^x, where a is the initial amount (in this case, 128 players), 0.5 is the common ratio representing a 50% reduction each round, and x is the round number. Therefore, the correct equation is y = 128(0.5)^x.
To provide further clarity, let's explore the given options:
- y = 128(2)^x - This would represent an exponential increase, not a decrease.
- y = 0.5^x * 128 - This is a more complex way of writing option 3, which is correct.
- y = 128(0.5)^x - This correctly models the situation, as it shows the number of players being halved every round (Option 3).
- y = -64x + 128 - This linear equation does not accurately model the exponential decrease of players.
Thus, the final answer to the student's question is Option 3.
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