e^-x Calculator

The e^-x Calculator is a simple yet powerful mathematical tool that computes the value of the exponential function e raised to the power of negative x. This function is widely used in areas such as probability, signal processing, physics, and finance. Specifically, e^-x represents exponential decay, which models things like radioactive decay, cooling processes, and discounting in financial models.

The calculator lets you enter a real number value for x and quickly computes the corresponding value of e^-x using precise mathematical algorithms. It’s especially helpful when working with equations or data that require high accuracy and instant computation without manually solving a series.

formula of e^-x Calculator

The general formula used by the calculator is:
e^(−x) = 1 / e^x

Where:
e is Euler’s number ≈ 2.718281828
x is the exponent (any real number)
e^(−x) is the result and represents exponential decay

This formula helps users understand how values decrease as x increases, which is the nature of decay in many real-world phenomena.

You can also use the series expansion to compute it manually:
e^(−x) = 1 − x + x²/2! − x³/3! + x⁴/4! − ...

This is the Taylor series expansion for e^-x and converges quickly for small values of x. However, using the calculator is much more efficient and accurate, especially for large values of x.

Common Values of e^-x

Here is a quick reference table for values of e^-x for common inputs:

x Value	e^-x (approximate)
0	1.000000
0.5	0.606531
1	0.367879
2	0.135335
3	0.049787
4	0.018316
5	0.006738
10	0.000045

This table is useful for quick estimations and helps visualize how fast the value of e^-x decreases as x increases.

Example of e^-x Calculator

Let’s say you want to calculate e^-2.5

Using the calculator:
e^-2.5 = 1 / e^2.5 ≈ 1 / 12.1825 ≈ 0.08208

So, the result of e^-2.5 is approximately 0.08208. This shows how a relatively small increase in the value of x leads to a significant reduction in the output.

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