How to use the EXP function
What is the EXP function?
The EXP function returns e raised to the power of a given number
What is e?
It is the base of the natural logarithm, ln. e is defined to be the limit of (1 + 1/n) raised to the nth power as n approaches infinity.
In equation form: e = lim (1 + 1/n)n as n -> infinity
The limit of this exponential growth pattern is the unique number e. For example:
(1 + 1/1)1 = 2
(1 + 1/2)2 = 2.25
(1 + 1/3)3 = 2.37037
The limit of this exponential growth pattern is the unique number e.
e = e1 equals 2.71828182845904.
e2 equals 7.389056099
What is ln?
ln is the natural logarithm and e is it's base.
eln x = x
ln ex = x
What applications has e?
- Logarithms to base e models growth/decay.
- Compound interest - e models exponential growth in finance.
- Probability theory - e features in Poisson distributions.
- Normal distributions - e in its probability density function.
- Euler's identity - e^ix = cos(x) + i*sin(x) links e with trigonometry and the imaginary unit i.
- Bacterial growth - The growth of bacterial populations can be modeled involving e.
- Mathematical constants - e is related to mathematical constants like π, φ and γ via infinite series and limits.
- Calculus - The derivative of e^x is itself e^x.
What logarithmic functions exist in Excel?
| Name | Excel Function | Description |
|---|---|---|
| Natural Logarithm | LOG(x) | Calculates the natural logarithm (base e) of x |
| Natural Logarithm | LN(x) | Same as LOG(x), calculates the natural log of x |
| Common Logarithm | LOG10(x) | Calculates the base 10 logarithm of x |
| Binary Logarithm | LOG2(x) | Calculates the base 2 logarithm of x |
| Exponentiation | POWER(x, y) | Raises x to the power of y |
| Exponential | EXP(x) | Raises e to the power of x |
Excel Function Syntax
EXP(number)
Arguments
| number | Required. The number used as an exponent to e. |
Formula in cell C3:
Comments
Graph of the natural exponential function.
Functions in 'Math and trigonometry' category
The EXP function function is one of many functions in the 'Math and trigonometry' category.
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