1. What is the Natural Exponential Function?

The natural exponential function, e^x, is one of the most important functions in mathematics. It describes exponential growth or decay and is the inverse of the natural logarithm function.

2. How Does the Calculator Work?

The calculator computes the exponential function:

Where:

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

Explanation: The function returns e raised to the power of x, which can represent continuous growth (when x > 0) or decay (when x < 0).

3. Importance of e^x Calculation

Details: The exponential function appears in many areas including compound interest, population growth, 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: e is an irrational number approximately equal to 2.71828. It's the base of natural logarithms.

Q2: What is e^0?
A: Any number raised to the power of 0 is 1, so e^0 = 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 e^x related to compound interest?
A: e appears in the limit of (1 + 1/n)^n as n approaches infinity, which models continuously compounded interest.

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