Math.E in JavaScript

 Math.E in JavaScript is a property of the Math object that provides the mathematical constant e (Euler's number), which is approximately equal to 2.71828. 

Euler's number is the base of the natural logarithm and is a fundamental constant in mathematics, especially in calculus and complex analysis.

How to Use Math.E

Math.E is used when you need the value of Euler's number in calculations, especially in exponential functions and logarithmic calculations. 

For example, it's useful in problems involving continuous growth or decay, such as in compound interest calculations or natural phenomena modeling.

Examples of Using Math.E

Here are 10 examples demonstrating how Math.E can be used in various JavaScript calculations:

// 1. Simple usage of Math.E
console.log("Math.E:", Math.E); // 2.718281828459045

// 2. Exponential Function (e^x)
let exponent = 2;
console.log("e^2:", Math.exp(exponent)); // 7.3890560989306495

// 3. Natural Logarithm of e (ln(e))
console.log("ln(e):", Math.log(Math.E)); // 1

// 4. Compound Interest Calculation
let principal = 1000; // Initial amount
let rate = 0.05; // 5% annual interest rate
let time = 3; // Time in years
let compoundInterest = principal * Math.pow(Math.E, rate * time);
console.log("Compound Interest:", compoundInterest); // 1157.6279931105455

// 5. Continuous Growth Example
let initialAmount = 500;
let growthRate = 0.02; // 2% growth rate
let growthTime = 10; // 10 time periods
let finalAmount = initialAmount * Math.exp(growthRate * growthTime);
console.log("Continuous Growth:", finalAmount); // 610.2693961083313

// 6. Exponential Decay
let decayRate = -0.03; // -3% decay rate
let decayTime = 5; // 5 time periods
let initialValue = 100;
let decayedValue = initialValue * Math.exp(decayRate * decayTime);
console.log("Exponential Decay:", decayedValue); // 86.14425858247785

// 7. Normal Distribution (Probability Density Function)
let mean = 0;
let stdDev = 1;
let x = 1;
let normalDistribution = (1 / (stdDev * Math.sqrt(2 * Math.PI))) * Math.exp(-0.5 * Math.pow((x - mean) / stdDev, 2));
console.log("Normal Distribution:", normalDistribution); // 0.24197072451914337

// 8. Growth Factor Calculation
let growthFactor = Math.exp(1);
console.log("Growth Factor (e^1):", growthFactor); // 2.718281828459045

// 9. Calculate Natural Logarithm of a Value
let value = 10;
let naturalLog = Math.log(value);
console.log("Natural Logarithm of 10:", naturalLog); // 2.302585092994046

// 10. Rate of Change in Exponential Functions
let initialValueChange = 50;
let rateChange = 0.1; // 10% rate of change
let timeChange = 4; // 4 time periods
let changedValue = initialValueChange * Math.exp(rateChange * timeChange);
console.log("Value with Rate of Change:", changedValue); // 74.53425441272612

Explanation of Examples

1. Simple Usage: Prints the value of Euler's number.
2. Exponential Function: Uses Math.exp() to compute e^2.
3. Natural Logarithm of e: Computes the natural logarithm of e, which is always 1.
4. Compound Interest Calculation: Uses Euler's number in the formula for continuous compounding interest.
5. Continuous Growth: Calculates final amount with continuous growth.
6. Exponential Decay: Computes the value after exponential decay.
7. Normal Distribution: Calculates the probability density function for a normal distribution.
8. Growth Factor: Computes the growth factor e^1.
9. Natural Logarithm of a Value: Computes the natural logarithm of a given value.
10. Rate of Change: Calculates the changed value after applying a growth rate over time.