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marriott country club plaza hotel kansas city - Sourci

📅 May 2, 2026 👤 scraface

May 02, 2026

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Question: An ornithologist observes a flock of birds migrating, where...
Solution: The number of birds follows a geometric sequence: $ 3, 6, 12...
The number of birds on day $ n $ is $ 3 \cdot 2^{n-1} $.
\cdot 2^{n-1} > 500
2^{n-1} > \frac{500}{3} \approx 166.67
Now compute powers of 2:
$ 2^7 = 128 $, $ 2^8 = 256 $
So $ 2^{n-1} > 166.67 $ implies $ n-1 \geq 8 $, thus $ n \geq 9 $.
On day 9, the count is $ 3 \cdot 2^8 = 3 \cdot 256 = 768 > 500 $.
On day 8: $ 3 \cdot 2^7 = 384 < 500 $, so day 9 is the first.

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