1. What is the Exponential Function?

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

2. How Does the Calculator Work?

The calculator computes the exponential function using the formula:

Where:

• \( e \) — Euler's number (~2.71828)
• \( x \) — The exponent value

Explanation: The function calculates e (Euler's number) raised to the power of the input value x.

3. Applications of Exponential Function

Details: The exponential function is used in compound interest calculations, population growth models, radioactive decay, and many physics equations.

4. Using the Calculator

Tips: Simply enter any real number as the exponent x. The calculator will compute e raised to that power.

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 natural logarithms.

Q2: What is e⁰?
A: Any number raised to the power of 0 equals 1, so e⁰ = 1.

Q3: What is the derivative of e^x?
A: The remarkable property of e^x is that its derivative is itself: d/dx(e^x) = e^x.

Q4: How is this different from general exponentiation?
A: This specifically calculates with base e, while general exponentiation can use any base.

Q5: What is e¹?
A: e¹ equals e, approximately 2.71828.