index number; index; exponent; exponential

简明释义

指数

英英释义

例句

1.Exponential growth can be modeled using the exponential (指数的) function.

指数增长可以用exponential (指数的) 函数建模。

2.In a database, each entry has a unique index (索引) to facilitate quick searches.

在数据库中，每个条目都有一个唯一的index (索引) 以便快速搜索。

3.The exponent (指数) in the equation determines how quickly the function grows.

方程中的exponent (指数) 决定了函数增长的速度。

4.The index number (索引号) of the product helps in tracking inventory efficiently.

产品的index number (索引号) 有助于有效地跟踪库存。

5.To calculate the interest, we need to find the index number (索引号) for the current rate.

要计算利息，我们需要找到当前利率的index number (索引号)。

作文

In mathematics, the concepts of index number (指数), index (索引), exponent (指数), and exponential (指数的) functions play a crucial role in understanding various phenomena. These terms are often intertwined, and grasping their meanings is essential for students and professionals alike. This essay will explore these concepts in detail and illustrate their significance through practical examples.Firstly, an index number is a statistical measure that represents the relative change in a variable or group of variables over time. For instance, in economics, index numbers are used to track inflation rates or changes in stock prices. By comparing the current value of a variable to its value in a base year, we can assess how much it has increased or decreased. This tool is invaluable for economists and policymakers as it provides a clear picture of economic trends and helps in making informed decisions.Secondly, the term index refers to a systematic arrangement of information, typically used to locate data quickly. In the realm of mathematics, an index can also refer to the notation used to represent the position of a number in a sequence. For example, in a mathematical expression, the index can indicate which element of a series we are examining. This concept is not only applicable in mathematics but also in various fields such as computer science, where indices are used to optimize data retrieval processes.The third term, exponent, is fundamental in mathematics, particularly in the study of powers. An exponent indicates how many times a number, known as the base, is multiplied by itself. For example, in the expression 2^3, the number 2 is the base, and 3 is the exponent. This means that 2 is multiplied by itself three times: 2 × 2 × 2 = 8. Understanding exponents is essential for mastering algebra and higher-level mathematics, as they form the basis for polynomial expressions and logarithmic functions.Finally, the term exponential refers to a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent. Exponential functions are characterized by their rapid growth or decay, depending on the value of the base. For instance, population growth can often be modeled using exponential functions, as populations tend to increase rapidly under ideal conditions. Understanding exponential growth is crucial in fields such as biology, economics, and environmental science, as it allows for predictions about future trends based on current data.In conclusion, the concepts of index number, index, exponent, and exponential functions are integral to various disciplines, especially in mathematics and economics. Mastering these terms not only enhances our understanding of mathematical principles but also equips us with the tools to analyze real-world situations effectively. As we continue to explore these concepts, we can appreciate their relevance and application in our daily lives, from tracking economic indicators to modeling population dynamics. Thus, a solid grasp of these terms is essential for anyone seeking to navigate the complexities of mathematics and its applications in the modern world.

在数学中，index number（指数）、index（索引）、exponent（指数）和exponential（指数的）函数的概念在理解各种现象中起着至关重要的作用。这些术语通常是交织在一起的，掌握它们的含义对于学生和专业人士来说都是必不可少的。本文将详细探讨这些概念，并通过实际例子说明它们的重要性。首先，index number 是一种统计测量，表示变量或一组变量随时间的相对变化。例如，在经济学中，index numbers 用于跟踪通货膨胀率或股票价格的变化。通过将当前变量的值与基年值进行比较，我们可以评估其增加或减少的幅度。这个工具对于经济学家和政策制定者来说是无价的，因为它提供了经济趋势的清晰图景，有助于做出明智的决策。其次，index 这个术语指的是信息的系统排列，通常用于快速定位数据。在数学领域，index 还可以指用于表示序列中数字位置的符号。例如，在一个数学表达式中，index 可以表示我们正在检查的系列的元素。这个概念不仅适用于数学，还适用于计算机科学等多个领域，其中 indices 被用来优化数据检索过程。第三个术语，exponent，在数学中尤其是幂的研究中是基础性的。exponent 表示一个数字（称为底数）被自身相乘多少次。例如，在表达式 2^3 中，数字 2 是底数，3 是 exponent。这意味着 2 自身相乘三次：2 × 2 × 2 = 8。理解 exponents 对于掌握代数和更高层次的数学至关重要，因为它们构成了多项式表达式和对数函数的基础。最后，exponential 这个术语指的是形如 f(x) = a * b^x 的数学函数，其中 'a' 是常数，'b' 是底数，'x' 是指数。Exponential 函数的特点是其快速增长或衰减，具体取决于底数的值。例如，人口增长通常可以用 exponential 函数建模，因为在人口理想条件下，人口往往会迅速增加。理解 exponential 增长对于生物学、经济学和环境科学等领域至关重要，因为它允许根据当前数据预测未来趋势。总之，index number、index、exponent 和 exponential 函数的概念在各个学科中，特别是在数学和经济学中，都是不可或缺的。掌握这些术语不仅增强了我们对数学原理的理解，而且使我们具备了有效分析现实世界情况的工具。随着我们继续探索这些概念，我们可以欣赏它们在日常生活中的相关性和应用，从跟踪经济指标到建模人口动态。因此，扎实掌握这些术语对于任何希望驾驭现代世界中数学复杂性的人来说都是至关重要的。