Find the Slowest Growing and the Fastest Growing Functions as X→∞

question 6

Multiple Choice

Find the slowest growing and the fastest growing functions as x→∞ .
- $$\begin{array} { l } y = e ^ { x } \\y = e ^ { x / 7 } \\y = x ^ { x } \\y = 4 ^ { x }\end{array}$$

• A) Slowest: \(y = e ^ { x / 7 }\)
• Fastest: \(\mathrm { y } = \mathrm { x } ^ { \mathrm { x } }\)
• B) Slowest: \(\mathrm { y } = \mathrm { e } ^ { \mathrm { x } / 7 }\) and \(\mathrm { y } = \mathrm { e } ^ { \mathrm { x } }\) grow at the same rate.
• Fastest: \(y = 4 ^ { x }\)
• C) Slowest: \(y = x ^ { x }\)
• Fastest: \(y = 4 ^ { x }\)
• D) Slowest: \(y = e ^ { x / 7 }\) and \(y = e ^ { x }\) grow at the same rate.
• Fastest: \(\mathrm { y } = \mathrm { x } ^ { \mathrm { x } }\)

Analyze the role and importance of sunk costs in economic and business decisions.

Understand the implications of fixed costs in the short and long term.

Distinguish between explicit and implicit costs in cost analysis.

Evaluate investment decisions taking into consideration the time value of money.

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Definitions:

Productive Capacity

The maximum output a system can produce over a given period under normal conditions, reflecting its efficiency and effectiveness.

Variable Costs

Costs that change in proportion to the level of activity or volume of production within a business.

Additional Processing Costs

Costs incurred when further processing is done on a product after an initial manufacturing phase, often enhancing its value.

Sales Value

Sales value refers to the total revenue generated from the sale of goods or services, before any deductions for costs or expenses.