1. What is the Exponential Function?

The exponential function \( e^x \) is one of the most important functions in mathematics, where e is Euler's number (approximately 2.71828). It describes exponential growth and decay in various scientific and mathematical applications.

2. How Does the Calculator Work?

The calculator uses the exponential function:

Where:

• \( e \) — Euler's number (~2.71828)
• \( x \) — Exponent value (dimensionless)

Explanation: The function calculates e (the base of natural logarithms) raised to the power of the input value x.

3. Importance of Exponential Calculation

Details: Exponential calculations are fundamental in mathematics, physics, engineering, finance, and many other fields. They are used to model population growth, radioactive decay, compound interest, and many natural phenomena.

4. Using the Calculator

Tips: Enter the exponent value (x) in the input field. The value can be positive, negative, or zero. 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 does e^0 equal?
A: Any non-zero number raised to the power of 0 equals 1, so e^0 = 1.

Q3: Can I calculate negative exponents?
A: Yes, the calculator handles both positive and negative exponent values.

Q4: What are some practical applications of e^x?
A: Used in compound interest calculations, population growth models, radioactive decay, and many physics equations.

Q5: How accurate is the calculation?
A: The calculator uses PHP's built-in exp() function which provides high precision results.