exp() function C++

The exp() function in C++ returns the exponential (Euler's number) e (or 2.71828) raised to the given argument.

Syntax for returning exponential e: result=exp()

Parameter: The function can take any value i.e, positive, negative or zero in its parameter and returns result in int, double or float or long double. Return Value: The exp() function returns the value in the range of [0, inf]. 

Error:

•  It shows error when we pass more than one argument in exp function 
• When the input value is too large, the exp function can return inf or nan as a result, indicating overflow.

Application: Given below is an example of application of exp() function 

#include <bits/stdc++.h>
using namespace std;

// function to explain use of exp() function
double application(double x)
{
    double result = exp(x);
    cout << "exp(x) = " << result << endl;
    return result;
}

// driver program
int main()
{
    double x = 10;
    cout << application(x);
    return 0;
}

exp(x) = 22026.5
22026.5

Time Complexity: O(1)
Auxiliary Space: O(1)

Here is the program to demonstrate the error in exp() function.

#include <bits/stdc++.h>
using namespace std;

// function to explain use of exp() function
double application(double x)
{
    double result = exp(x);
    cout << "exp(x) = " << result << endl;
    return result;
}

// driver program
int main()
{
    double x = 1000;
    cout << application(x);
    return 0;
}

exp(x) = inf
inf

Time Complexity: O(1)
Auxiliary Space: O(1)

Applications of e (mathematical constant):

• Compound Interest : An account that starts at $1 and offers an annual interest rate of R will, after t years, yield e^Rt dollars with continuous compounding (Here R is the decimal equivalent of the rate of interest expressed as a percentage, so for 5% interest, R = 5/100 = 0.05)
• Value of below expression is e. \lim _{n\to \infty }\left(1+{\frac {1}{n}}\right)^{n}.
• The probability that a gambler never wins if he/she tries million times in a game where chances of winning in every trial is one by million is close to 1/e.
• The number e is the sum of the infinite series e=\sum _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{0!}}+{\frac {1}{1!}}+{\frac {1}{2!}}+{\frac {1}{3!}}+{\frac {1}{4!}}+\cdots \,,

Source : Wiki