Multiplicative
Subtype of MethodThe r numbers a₁ , a₂ , ... , aᵣ specified through the key Amount represent the factors by which the elements of the sequence x₁ , x₂ , ... , xᵤ are multiplied in order to produce their successive elements, where:
x₁ is the given externally provided seed number
and
x₁ , x₂ , ... , xᵤ is the requested sequence of u numbers
Formally:
x₂ = a₁ x₁
x₃ = a₂ x₂
...
xᵤ = aᵤ₋₁ xᵤ₋₁
If u - 1 > r, the above formulas still hold under the usual flat extension assumption whereby the extra elements aᵣ₊₁ , aᵣ₊₂ , ... , aᵤ₋₁ are introduced and set all equal to the last number aᵣ
In the common case of r = 1, i.e. when only one number a is defined through the key Amount, the above relations simplify to:
x₂ = a x₁
x₃ = a x₂
...
xᵤ = a xᵤ₋₁
An example for the latter case is a = 1.2, which means that each number is produced by multiplying its predecessor by the factor 1.2
It is obvious that the case a = 1.2 leads to the same effect as the choice Percentage combined with a = 0.2
It is also obvious that if a = 1, this amounts to the same effect as the choice No Change