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A local tennis club raises money by hosting an annual tournament. The tournament starts with 128 players enter. Each round eliminates half of the players. What is the exponential decay function for this situation? O f(x) = 128" o f(x) = (금)- O f(z) = 128 O f(2) %=D 128(글) %3D

A local tennis club raises money by hosting an annual tournament. The tournament starts with 128 players enter. Each round eliminates half of the players. What is the exponential decay function for this situation? O f(x) = 128" o f(x) = (금)- O f(z) = 128 O f(2) %=D 128(글) %3D

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Exponential Decay in a Tennis Tournament A local tennis club raises money by hosting an annual tournament. The tournament starts with 128 players. Each round eliminates half of the players. What is the exponential decay function for this situation? **Select the correct exponential decay function:** 1. \( f(x) = 128^x \) 2. \( f(x) = \left( \frac{1}{2} \right)^x \) 3. \( f(x) = \frac{1}{2} \cdot 128^x \) 4. \( f(x) = 128 \left( \frac{1}{2} \right)^x \) **Explanation:** - **Option 1**: This function indicates exponential growth, not decay. - **Option 2**: This function represents decay rate without initial amount. - **Option 3**: This function represents fractional decay with an incorrect structure for this context. - **Option 4**: Correct! This option represents the initial number of players (128) multiplied by the decay factor \(\left( \frac{1}{2} \right)^x\) which shows the halving of players each round. Understanding this concept helps in modelling situations where quantities reduce by a consistent factor over each time period. In our example, 'x' represents the number of rounds.
Transcribed Image Text:### Exponential Decay in a Tennis Tournament A local tennis club raises money by hosting an annual tournament. The tournament starts with 128 players. Each round eliminates half of the players. What is the exponential decay function for this situation? **Select the correct exponential decay function:** 1. \( f(x) = 128^x \) 2. \( f(x) = \left( \frac{1}{2} \right)^x \) 3. \( f(x) = \frac{1}{2} \cdot 128^x \) 4. \( f(x) = 128 \left( \frac{1}{2} \right)^x \) **Explanation:** - **Option 1**: This function indicates exponential growth, not decay. - **Option 2**: This function represents decay rate without initial amount. - **Option 3**: This function represents fractional decay with an incorrect structure for this context. - **Option 4**: Correct! This option represents the initial number of players (128) multiplied by the decay factor \(\left( \frac{1}{2} \right)^x\) which shows the halving of players each round. Understanding this concept helps in modelling situations where quantities reduce by a consistent factor over each time period. In our example, 'x' represents the number of rounds.
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