1. What is e^5?

e^5 (e to the power of 5) is the exponential function with base e (Euler's number, approximately 2.71828) raised to the power of 5. It represents continuous growth at a rate of 100% over 5 units of time.

2. How Does the Calculator Work?

The calculator uses the exponential function:

Where:

• \( e \) — Euler's number (~2.71828)
• \( x \) — The exponent (5 in this case)

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

3. Importance of Exponential Function

Details: The exponential function is fundamental in mathematics, appearing in compound interest, population growth, radioactive decay, and many other natural processes.

4. Using the Calculator

Tips: Enter any exponent value to calculate e raised to that power. The default value is 5 (e^5).

5. Frequently Asked Questions (FAQ)

Q1: What is the approximate value of e^5?
A: e^5 ≈ 148.413159

Q2: What is the relationship between e^x and natural logarithm?
A: The natural logarithm (ln) is the inverse function of e^x. If y = e^x, then x = ln(y).

Q3: Where is e^5 used in real life?
A: It appears in continuous compounding interest calculations, population growth models, and physics equations.

Q4: How is e^5 different from 5^e?
A: e^5 is e multiplied by itself 5 times (~148.413), while 5^e is 5 multiplied by itself e times (~79.432).

Q5: Can I calculate negative exponents?
A: Yes, e^-x equals 1/e^x, representing exponential decay rather than growth.