Name the inhibitor

You will write three things. The first is the rate of an enzyme with an inhibitor. The second is a function that names the kind of inhibitor from two pairs of numbers. The third is the substrate level that overcomes a competitive inhibitor.

The idea. A competitive inhibitor multiplies $K_m$ by $1 + i$ and leaves $V_{\max}$ alone. A non-competitive inhibitor divides $V_{\max}$ by $1 + i$ and leaves $K_m$ alone. Here $i = [I]/K_i$.

Your tasks.

1. In rate, return the rate for kind equal to "none", "competitive" or "non-competitive".
2. In classify, return "competitive", "non-competitive" or "neither". Call a change real when it is more than 10 % of the value.
3. Set needed to the substrate concentration that gives half of the free $V_{\max}$ with a competitive inhibitor at i.