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 processes found in various scientific and financial applications.

2. How Does the Calculator Work?

The calculator uses the exponential function:

Where:

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

Explanation: The function calculates e raised to the power of the input value x, representing continuous exponential growth.

3. Importance of Exponential Calculation

Details: Exponential calculations are crucial in compound interest calculations, population growth modeling, radioactive decay, and many physics and engineering applications involving natural growth processes.

4. Using the Calculator

Tips: Enter any real number as the exponent value. The calculator will compute e raised to that power with high precision.

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 appears naturally in continuously compounded interest formulas: A = Pe^(rt), where P is principal, r is rate, and t is time.

Q5: Can e^x be negative?
A: No, e^x is always positive for all real values of x, though it approaches 0 as x approaches negative infinity.