**Title: Understanding Asymptotic Growth Rates****Instructions:**Choose the correct order of the following functions by asymptotic growth rate, from smaller to bigger.**Note:** Your answer should look like a sequence of numbers such as 1 2 3 4 5 6.1. **Function 1:** \( n^2 \)2. **Function 2:** \( (2)^n \)3. **Function 3:** \( \log n \)4. **Function 4:** 105. **Function 5:** \( 8^{\log n} \)6. **Function 6:** \( n! \)**Explanation:**The task is to determine the asymptotic growth rate of these functions, ranking them from the smallest to the largest as \( n \) approaches infinity.

Answered: Image /qna-images/answer/a3b134b4-c4f0-48f5-b214-0d3b76027c94.jpg

Choose the correct order of the following functions by asymptotic growth rate (smaller to bigger) Note: answer looks like 1 2 3 4 5 6 function 1: n² function 2: (2) function 3: Ign function 4: 10 function 5:8lgn function 6: n!

Choose the correct order of the following functions by asymptotic growth rate (smaller to bigger) Note: answer looks like 1 2 3 4 5 6 function 1: n² function 2: (2) function 3: Ign function 4: 10 function 5:8lgn function 6: n!

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

**Title: Understanding Asymptotic Growth Rates**

**Instructions:**

Choose the correct order of the following functions by asymptotic growth rate, from smaller to bigger.

**Note:** Your answer should look like a sequence of numbers such as 1 2 3 4 5 6.

1. **Function 1:** \( n^2 \)

2. **Function 2:** \( (2)^n \)

3. **Function 3:** \( \log n \)

4. **Function 4:** 10

5. **Function 5:** \( 8^{\log n} \)

6. **Function 6:** \( n! \)

**Explanation:**

The task is to determine the asymptotic growth rate of these functions, ranking them from the smallest to the largest as \( n \) approaches infinity.

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