Please answer the question in the screenshot. Please give full reasoning for the solution. **Understanding Function Growth Rates**The following functions have different growth rates (i.e., as \( n \) increases by 1, \( T(n) \) may increase to different extents depending on what \( T(n) \) is). List the following functions by growth rate in increasing order.- \( T_1 = 20n \)- \( T_2 = n^2 + 2n \)- \( T_3 = n^2 + 10\log_2 n \)- \( T_4 = 2^n \)### Explanation:1. **\( T_1 = 20n \)** - This function grows linearly with \( n \). As \( n \) increases, \( T_1 \) increases proportionally.2. **\( T_2 = n^2 + 2n \)** - This function is a quadratic function because the \( n^2 \) term will dominate as \( n \) becomes large.3. **\( T_3 = n^2 + 10\log_2 n \)** - Although this function has a logarithmic component, the \( n^2 \) term will dominate as \( n \) becomes large, making it essentially a quadratic function.4. **\( T_4 = 2^n \)** - This function is exponential, which grows much faster than polynomial functions for large \( n \).### Ordered Growth Rates:From the slowest growth rate to the fastest:\[ T_1 < T_2 \approx T_3 < T_4 \]#### Detailed Explanation of Growth:- **Linear Growth (\( T_1 = 20n \))**: The simplest growth pattern, where the function increases by a constant amount as \( n \) increases. - **Quadratic Growth (\( T_2 \) and \( T_3 \))**: These functions increase much more quickly than linear functions because their dominant term is \( n^2 \). Although \( T_2 \) and \( T_3 \) may seem different, the additional \( 2n \) and \( 10\log_2 n \) terms are insignificant relative to the \( n^2 \) term for large \( n \).- **Exponential Growth (\( T_4 = 2^n \))**: This

We are given some functions and we are going to arrange them in increasing order of their growth.…

The following functions have different growth rate (i.e., as n increases by 1, T(n) may increase to different extents depending or what T(n) is). List the following functions by growth rate in increasing order. • T1 = 20n • T2 = n² + 2n T. = n2 + 101ogn

The following functions have different growth rate (i.e., as n increases by 1, T(n) may increase to different extents depending or what T(n) is). List the following functions by growth rate in increasing order. • T1 = 20n • T2 = n² + 2n T. = n2 + 101ogn

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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