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: \(\mathrm { y } = \mathrm { x } ^ { \mathrm { x } }\)

---

Definitions:

Operating Expenses

Costs associated with running the day-to-day operations of a business which are necessary to keep the business functioning, excluding the cost of goods sold.

Gross Profit

The distinction between the income from sales and the expense of goods sold prior to subtracting costs for overheads, wages, taxes, and interest.

Cost of Goods Sold

This is an accounting term that refers to the direct costs attributable to the production of the goods sold by a company.

Income from Operations

Revenue from a company's everyday business activities minus the costs and expenses associated with those operations.