Use Mathematical Induction to Prove That $1 + 2 ^ { n } \leq 3 ^ { n } \text { for all } n \geq 1$

question 48

Essay

Use mathematical induction to prove that $1 + 2 ^ { n } \leq 3 ^ { n } \text { for all } n \geq 1$

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Definitions:

Decoupling Function

describes the practice of separating different parts of a production process so that a delay or failure in one area does not directly impact another, enhancing flexibility and reliability.

Quantity Discount Problem

A pricing strategy issue where the cost per item lowers as the quantity purchased increases, necessitating analysis for optimal purchasing decisions.

Setup Cost

The expenses incurred to prepare equipment, machinery, or a production line for the manufacture of a new batch of goods.

Holding Cost

The expenses associated with storing unsold goods or materials, including warehousing, insurance, and opportunity costs.