The PCR counter

You will write three small functions that count the molecules in a PCR tube.

The idea. With an efficiency $e$ in every cycle, the number is multiplied by $1 + e$. With $e = 1$ it doubles. For A-Level and IB, the number of molecules of exactly the wanted length after $n$ cycles, from one template, is $2^n - 2n$.

Your tasks.

1. Finish molecules. It gives the number after cycles cycles, from the start, the cycles and the efficiency.
2. Finish cycles_needed. It gives the smallest number of cycles with a perfect efficiency that makes the number reach the target.
3. Finish exact_length. It gives the number of molecules of exactly the wanted length after cycles cycles from one template.