How to use the EXP function
What is the EXP function?
The EXP function returns e raised to the power of a given number.
Table of Contents
1. Introduction
What is e?
It is the base of the natural logarithm, ln.
The chart above shows the curve of ex, 2x, and 10x
What is the definition of e?
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 approx. 2.71828182845904.
e2 equals approx. 7.389056099
What is the EXP function in Excel an abbreviation of?
The "EXP" name refers to Exponent or Exponential.
What is ln?
ln is the natural logarithm and e is it's base.
eln x = x
ln ex = x
What are the key exponential rules?
- Product of Powers
e^x * e^y = e^(x+y)
When two numbers with exponents are multiplied together, and the bases are the same, you add the exponents.
Example, e5 * e10 = e(5+10) - Quotient of Powers
e^x / e^y = e^(x-y)
Two numbers with exponents are divided and the bases are the same you subtract the exponents.
Example, e10 / e5 = e(10-5) - Power of Powers
(e^x)^y = e^(x*y)
If a base is raised to a power and the entire expression is further raised to another power then the two powers are multiplied, and the base remains unchanged.
Example, (e10)5 = e(10*5) - Power of Product
(ey)^x = e^x * y^x
When a product expression within parentheses is raised to an exponent, each element within the product is raised to that exponent individually.
Example, (5*e)10 = e10 * e5 - Negative Exponent
e^-x = 1/e^x
A negative exponent indicates that the base should be taken as the reciprocal and raised to the positive equivalent of the exponent.
Example, e-x = 1/ex - Fractional Exponent
e^(1/x) = x√e
A number raised to a fractional exponent is equivalent to taking the root of that number.
Example, e(1/x) = x√e
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 |
2. EXP Function Syntax
EXP(number)
3. EXP Function Arguments
number | Required. The number used as an exponent to e. |
4. EXP Function Example
Formula in cell C3:
Graph of the natural exponential function.
Functions in 'Math and trigonometry' category
The EXP function function is one of 73 functions in the 'Math and trigonometry' category.
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