math.exp()

The math.exp() function computes the value of the mathematical constant ( e ) (approximately 2.718) raised to the power of a given number. It is commonly used in exponential growth, decay calculations, and other mathematical applications.

Syntax

math.exp(`x`)

Parameters

Return Value

Returns the result of ( e^x ), where ( e ) is the base of the natural logarithm (approximately 2.718).

• If x is 0, the function returns 1 (since ( e^0 = 1 )).
• If x is a negative number, the function returns the reciprocal of \( e^{|x|} \).
• If x is invalid or non-numeric, the function returns nil.

Examples

Example 1: Basic Exponentiation

Compute \( e^x \) for a positive number.

local result = math.exp(1)
print(result)

-- Output: 2.718281828459

Example 2: Zero as the Exponent

Compute ( e^0 ).

local result = math.exp(0)
print(result)

-- Output: 1

Example 3: Negative Exponents

Calculate \( e^{-x} \) for a negative number.

local result = math.exp(-1)
print(result)

-- Output: 0.36787944117144

Example 4: Exponentiation with Larger Numbers

Compute \( e^x \) for a larger value of \( x \).

local result = math.exp(5)
print(result)

-- Output: 148.41315910258

Example 5: Small Values of \( x \)

Compute ( e^x ) for small positive numbers.

local result = math.exp(0.1)
print(result)

-- Output: 1.1051709180756

Use Cases

• Exponential Growth and Decay: Calculate compound growth or decay over time.
• Mathematical Modeling: Solve problems involving the natural exponential function.
• Logarithms and Inverses: Use in conjunction with math.log() for inverse operations.

See also

• math.log(): Calculates the natural logarithm of a number, the inverse of math.exp().
• math.pow(): Computes the result of raising any base to a power.
• math.sqrt(): Computes the square root of a number, useful for related calculations.