Algorithm to map an interval to a smaller interval

Question

I tried searching, but due to the nature of my question, I was unable to find something satisfactory.

My problem is the following: I am trying to map numbers ranging fro

Answer 1

I think that instead of giving you a formula of direct mapping, a better approach would be to explain the idea behind it:

Suppose we want to map an interval [0,1] to interval [1,3], which can be seen as the problem of finding f(x) = Ax + B such that giving any x from interval [0,1], will result in f(x) being/resulting in interval [1,3].

From this perspective, we already know some values:

1. x = 0 & f(0) = 1 => f(0) = A*0 + B = 1 => B = 1
2. x = 1 & f(1) = 3 => f(1) = A*1 + B = 3 <=> A + 1 = 3 => A=2

From (1) and (2), we may conclude that the function that maps interval [0,1] to [1,3] is f(x) = 2x + 1.

In you very case, you now should have all necessary knowledge to be able to map [0,2000] interval to [10,100].