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Exponential Calculator

(a number)



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How to use this Exponential Calculator 🤔

  1. Enter ✎ value for a number (x).
  2. As soon as you enter the required input value(s), the Exponential is calculated immediately, and displaed in the output section (present under input section).

Calculating the Exponential of a Number

In mathematics, the exponential function is a mathematical function denoted as \(e^x\), where \(e\) is the base of natural logarithms, approximately equal to 2.71828. The exponential function is widely used in various fields such as calculus, complex analysis, and in describing growth processes.

The expression \(e^x\) represents the value of the constant \(e\) raised to the power of \(x\). This function grows rapidly as the value of \(x\) increases and is fundamental in many mathematical models.

For example, the expression \(e^3\) represents the value of \(e\) raised to the power of 3:

\(e^3\)

Using a calculator or mathematical software, this value is approximately equal to 20.0855.

Examples

Let’s explore some examples to understand how to calculate the exponential of a number.

1. Calculate the value of \(e^3\).

Answer

First, we identify the given value:

Given:

  • Exponent (x): 3

Next, we calculate the value of \(e\) raised to the power of 3:

Steps:

  • \(e^3\)
  • Using a calculator, the value is approximately 20.0855.

Result:

∴ The value of \(e^3\) is approximately 20.0855.

2. Calculate the value of \(e^2\).

Answer

We start by identifying the given value:

Given:

  • Exponent (x): 2

Next, we calculate the value of \(e\) raised to the power of 2:

Steps:

  • \(e^2\)
  • Using a calculator, the value is approximately 7.3891.

Result:

∴ The value of \(e^2\) is approximately 7.3891.

3. Determine the value of \(e^0\).

Answer

First, we identify the given value:

Given:

  • Exponent (x): 0

Next, we calculate the value of \(e\) raised to the power of 0:

Steps:

  • \(e^0\)
  • By definition, any number raised to the power of 0 is 1.

Result:

∴ The value of \(e^0\) is 1.

4. Calculate the value of \(e^{-1}\).

Answer

We start by identifying the given value:

Given:

  • Exponent (x): -1

Next, we calculate the value of \(e\) raised to the power of -1:

Steps:

  • \(e^{-1}\)
  • Using a calculator, the value is approximately 0.3679.

Result:

∴ The value of \(e^{-1}\) is approximately 0.3679.