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Home » Calculate the final population using the formula for exponential growth: - Feedz API

Calculate the final population using the formula for exponential growth: - Feedz API

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 Since the slots are indistinct, we count partitions of the set of 4 satellites into at most 2 non-empty indistinct subsets. We consider all partitions of 4 labeled objects into 1 or 2 non-empty indistinct subsets.

📌 Partitions into 1 subset: only $1$ way — all satellites in one slot.

📌 Partitions into 2 non-empty indistinct subsets: this is the number of equivalence classes under swapping, given by the Stirling number of the second kind $S(4,2)$, which counts the number of ways to partition 4 distinguishable objects into 2 non-empty indistinct subsets.

📌 We compute $S(4,2)$:

📌 $S(4,2) = 2^2 - 1 = 7$? No — standard recurrence:

📌 $S(3,2) = 2 \cdot 1 + 1 = 3$

📌 Alternatively: list all such partitions:

📌 $\{1,2,3\}, \{4\}$

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