Let

question 46

Essay

Let $a _ { 1 } = 2 , a _ { 2 } = 9 \text {, and } a _ { n } = 2 a _ { n - 1 } + 3 a _ { n - 2 } \text { for } n \geq 3 \text {. Show that } a _ { n } \leq 3 ^ { n } \text { for all positive integers } n \text {. }$

---

Definitions:

Common Fixed Expenses

Costs that remain constant regardless of the volume of goods produced or sold, including items like lease payments, wages, and coverage fees.

Break-Even

The point at which total costs equal total revenue, resulting in neither profit nor loss.

Sales Dollars

The total monetary amount received from selling goods or services before any deductions are made.

Absorption Costing

An accounting method that includes all manufacturing costs, both variable and fixed, in the calculation of the cost per unit of goods produced.