Calculate a Repeated Multiplication
Calculator for the repeated multiplication or division, e.g. doubling, triplication, bisection. This is called potentiation. A start value is is multiplied by a value b, for instance doubled (b=2) or divided in half (b=0.5). This happens c times in a row. A table with all the intermediate results and the end result is shown or only the end result.
The formula for the potentiation is: xc = a * b c
A doubling with the start value 1, the power of two, occurs frequently, like at cell division or for computer memory. This is preselected as an example.
Repeated multiplication is a colloquial term for exponential calculation. This type of calculation is characterized by the fact that, in the case of growth, it starts slowly and then gets faster and faster. Mathematically, this leads to increasingly steep curves. In reality, however, an exponentially growing system will eventually reach limits that prevent further growth. Where these limits lie depends on the system. People are not used to dealing mentally with exponential growth. We often expect things to continue as they have developed so far, which is not the case with repeated multiplication. One example is the spread of a disease in an epidemic, where it is possible to estimate early on how quickly it will spread, but awareness of this is slow to gain acceptance. With this type of growth, the upper limit of the spread is reached when all possible cases are infected or immunized; a slowdown occurs long before that. In the case of diseases, the factor is the basic reproduction number, which indicates how many other people a carrier of the disease infects on average. For influenza this value is around 1 to 2, and for measles around 15.