1. What is the Exponential Function?

The exponential function e^x (where e ≈ 2.71828 is Euler's number) is one of the most important functions in mathematics. It describes exponential growth and decay processes found in nature, finance, physics, and many other fields.

2. How Does the Calculator Work?

The calculator uses the exponential function:

Where:

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

Explanation: The function calculates e raised to the power of x, representing continuous growth/decay at a rate proportional to the current value.

3. Importance of Exponential Calculation

Details: Exponential calculations are essential in compound interest calculations, population growth modeling, radioactive decay, signal processing, and many scientific and engineering applications.

4. Using the Calculator

Tips: Enter any real number as the exponent value. The calculator will compute e raised to that power. Both positive and negative values are supported.

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

Q3: What is the derivative of e^x?
A: The derivative of e^x is e^x, making it the unique function that is its own derivative.

Q4: How is e^x related to compound interest?
A: e^x represents continuous compounding, where x is the interest rate multiplied by time.

Q5: Can I calculate negative exponents?
A: Yes, e^(-x) = 1/e^x, which represents exponential decay rather than growth.