1. What is the Natural Exponential Function?

The natural exponential function, y = e^x, is one of the most important functions in mathematics. It describes exponential growth or decay and appears in many areas of science, finance, and engineering.

2. How Does the Calculator Work?

The calculator computes the natural exponential function:

Where:

• \( y \) — Output value (unitless)
• \( e \) — Euler's number (~2.71828)
• \( x \) — Input value (unitless)

Explanation: The function calculates e raised to the power of the input value x.

3. Importance of Exponential Function

Details: The natural exponential function is fundamental in calculus, differential equations, compound interest calculations, population growth models, and radioactive decay.

4. Using the Calculator

Tips: Simply enter any real number as the input value x. The calculator will compute e^x. Both positive and negative values are valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the value of e?
A: Euler's number e is approximately 2.71828 and is the base of the natural logarithm.

Q2: What's special about e^x?
A: It's the unique function that equals its own derivative, making it fundamental in calculus.

Q3: What does e^0 equal?
A: Any number raised to the power of 0 equals 1, so e^0 = 1.

Q4: How is this different from regular exponentiation?
A: This uses the special base e, while regular exponentiation can use any base.

Q5: What are practical applications of e^x?
A: Used in compound interest, population growth, radioactive decay, heat transfer, and many physics/engineering applications.