1. What is the Exponential Function?

The exponential function, denoted as exp(x) or e^x, is one of the most important functions in mathematics. It describes exponential growth and decay processes and appears in various scientific and engineering applications.

2. How Does the Calculator Work?

The calculator uses the exponential function formula:

Where:

• \( x \) — Input value (dimensionless)
• \( e \) — Euler's number (approximately 2.71828)

Explanation: The function calculates e raised to the power of x, where e is the base of the natural logarithm.

3. Applications of Exponential Function

Details: The exponential function is used in compound interest calculations, population growth models, radioactive decay, signal processing, and many other scientific and financial applications.

4. Using the Calculator

Tips: Enter any real number value for x. 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 is exp(0)?
A: exp(0) = e^0 = 1. Any number raised to the power of 0 equals 1.

Q3: What is exp(1)?
A: exp(1) = e^1 = e ≈ 2.71828.

Q4: How does the function behave for negative values?
A: For negative x values, exp(x) represents exponential decay and produces values between 0 and 1.

Q5: What are some real-world applications?
A: Exponential functions model population growth, radioactive decay, compound interest, cooling processes, and many natural phenomena.