What is the approximate value of the constant e?

The constant e is an important mathematical constant that serves as the base for natural logarithms. Its approximate value is 2.71828. This value arises in various mathematical contexts, particularly in calculus, where it is used in functions involving growth and decay, such as compound interest and population growth models.

The significance of e stems from its unique properties in calculus, especially in relation to the derivative of the exponential function. The function e^x is special because it is equal to its own derivative, making it a fundamental component in mathematical analysis.

Thus, the option of 2.71828 accurately represents the constant e, while the other values correspond to different mathematical constants. For example, 3.14159 is the value of π (pi), which relates to circle geometry, and 1.41421 is the square root of 2, significant in geometry and algebra. The value 2.64575 does not correspond to a notable mathematical constant. Understanding the distinct numerical identities of these constants is crucial in applied algebra and other areas of mathematics.