“exponential function to base a”的概念、定义、习题解题方法及翻译-数学辞典

单词

exponential function to base a

释义

exponential function to base a

Let a be a positive number not equal to 1. The exponential function to base a is the function f such that f(x) = a^x for all x in R. The graphs y = 2^x and $inline$ illustrate the essential difference between the cases when a>1 and a<1. See also exponential decay, exponential growth.

Graph showing exponential growth

Graph showing exponential decay

As x may not be an integer (or rational number even) a^x may not be defined as ‘a multiplied by itself x times' and instead is defined by

This definition still satisfies rules (i)–(vii) of the rules for indices (see index). Further, by the chain rule,

$inline$

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数学辞典收录了4151条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。