Enter a value (x) into the calculator below to calculate the value of e^-x. e is also known as Euler’s number which is equal to approximately 2.71828.

 e^-x Formula

The following formula is used by the calculator above to determine the value of e^-x.

Since e is a known value, also known as Euler’s number, which is approximately 2.71828, this calculator can simply take that number and raise it to the negative value of X.

How to calculate e^-x.

Calculating e^-x is as simple as raising the number 2.7182 to the inverse of the variable x.

FAQ

Why is e^-x important in mathematics and science? The function e^-x is crucial because it describes exponential decay, which is a common pattern in various natural processes such as radioactive decay, cooling, and more. It’s also used in finance to model depreciation and in differential equations that describe many physical phenomena.

Can e^-x ever be zero? No, e^-x can never be zero. The function e^-x approaches zero as x approaches infinity, but it will never actually reach zero. This is because e^x (where x is any real number) is always positive, and thus its inverse (e^-x) is also always positive, though it can get arbitrarily close to zero.

How do calculators compute e^-x with high precision? Calculators and computers use series expansions, such as the Taylor Series or the Maclaurin Series, to compute e^-x to a high degree of accuracy. These methods approximate e^-x by summing a finite number of terms from an infinite series, which gets closer to the true value as more terms are added.

Is there a difference between e^-x and the inverse of e^x? Mathematically, e^-x and the inverse of e^x are the same. The notation e^-x is a way to express the multiplicative inverse (or reciprocal) of e^x, which means they are two different ways to represent the same mathematical relationship.