The `exp()`

function in the C programming language, provided through the `math.h`

header, calculates the base-e exponential of a given number. This function is pivotal in scientific computing, financial calculations, and anywhere exponential growth or decay factors into an algorithm.

In this article, you will learn how to effectively utilize the `exp()`

function in various programming scenarios. Discover how this function can be applied across different contexts to compute exponential values efficiently and accurately.

Recognize that

`exp()`

computes the exponential of a number with base e, which is approximately 2.71828.Note that the prototype of

`exp()`

found in`math.h`

is as follows:cdouble exp(double x);

This function takes a double precision floating-point number and returns the exponent of

`e`

raised to the power of this number.

Include the

`math.h`

header to access the`exp()`

function in your C program.Prepare a double value and use

`exp()`

to calculate its exponential.c#include <stdio.h> #include <math.h> int main() { double value = 1.0; double result = exp(value); printf("e^1.0 = %f\n", result); return 0; }

In this code,

`exp()`

calculates the exponential of`1.0`

, which is the base`e`

. The result is printed on the console.

Understand that the formula for continuous compounding can be expressed using the exponential function: ( A = P e^{rt} ), where:

- ( A ) is the amount of money accumulated after n years, including interest.
- ( P ) is the principal amount.
- ( r ) is the annual interest rate (decimal).
- ( t ) is the time the money is invested for in years.

Implement the formula using

`exp()`

in a C program.c#include <stdio.h> #include <math.h> int main() { double principal = 1000; // Initial investment double rate = 0.05; // Annual interest rate double time = 10; // Time in years double amount = principal * exp(rate * time); printf("Amount after %f years is %f\n", time, amount); return 0; }

This snippet calculates the amount accumulated over 10 years with a 5% interest rate compounded continuously.

Learn that exponential decay models often use the

`exp()`

function to describe the decrease in quantity over time.Code a C function simulating exponential decay.

c#include <stdio.h> #include <math.h> int main() { double initialAmount = 1000; // Initial quantity double decayRate = 0.3; // Decay rate double time = 5; // Time double remainingAmount = initialAmount * exp(-decayRate * time); printf("Remaining amount after %f years is %f\n", time, remainingAmount); return 0; }

Here,

`exp()`

is used to model the decay of a quantity over 5 years with a decay rate of 0.3 per year.

The `exp()`

function in C, accessible through `math.h`

, is an indispensable tool for computing exponential values swiftly and precisely. Whether you are modelling financial forecasts, natural decay processes, or any scenario where exponential change is a factor, `exp()`

offers a reliable and straightforward solution. By integrating the examples provided, enhance your programs to handle complex calculations with ease and efficiency.