The graph was compiled using our online tool. As you can see by step 10 an exponential process that started with a base of 2 is completely dwarfed by one started with a base of 3 to such an extent that the base 2 line looks almost like a flat line next to the base 3 exponential curve, which is why we had to provide a zoom-in. In the graph above, you can think of each exponent as a generation (in biology), or as a tier of people who have seen a viral video or read a viral article (in marketing), or the power released from an earthquake of a magnitude equal to the exponent. ![]() The decibel scale used to measure volume is also exponential: 20 dB = 10 2 dB = 100 power ratio, 30 dB = 10 3 = 1,000 power ratio, so a 30 dB sound level is 10 times louder than a 20 dB sound level. The scale for measuring Earthquakes is also exponential, so a magnitude 5 earthquake is 32 times stronger than a magnitude 4 earthquake (10 1.5), while a magnitude 6 earthquake releases 1,000 times more energy (10 3) than a 4. Moore's law about the increase of computing power is in essence an exponential law. ![]() we talk about exponentially increasing reach. In marketing and the spreading of ideas, memes, viral videos, etc. In physics we have exponential decay related to light, sound, gravity, dangerous chemicals, and radiation (see radioactive decay & half-life). Practitioners of these disciplines often end up using an exponential calculator. compound interest), biology (population growth is often exponential), chemistry, physics, and, of course - computer science where storage capacity units are traditionally based off the powers of two, while public-key cryptographic functions rely on the hard reversibility of exponentiation. Practical application of exponentsĮxponentiation has uses in economics (e.g. An exponent with base 0 does not technically exist, so it is not supported by our exponent calculator. The formula for exponentiation is: where n is the exponent and b is the base. You can use our permutation calculator for these calculations as well. In combinatorics exponents express the number of possible permutations, that is - how many unique ways there are to select a part of a collection, or a set of things in which the order matters. The most commonly computed exponents are the square of a number (b 2, b raised to the second power / b to the power of two) and the cube of a number (b 3, b raised to the 3-rd power / b to the power of 3), and their inverse functions: square root and cube root.Įxponents are related to logarithms so that the natural logarithm ln(e) is the inverse of the exponential function b e, however defining exponentiation using logarithms is more common when dealing with complex numbers. If the exponent is a negative, for example -5, the operation is 1 divided by the base raised to the absolute value of the exponent: b -5 = 1 / b 5. When the exponent is a positive integer the operation is equal to multiplying the base by itself e times. This is the operation this online exponent calculator performs for you. The exponent is usually written as a superscript, for example if the base is b and the exponent e the exponentiation of b by e will be b e. ![]() How to calculate exponents?Įxponentiation is a mathematical operation in which a number called the base is raised to a power, which is given by the exponent. How to calculate exponents?Įxponentiation.
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