Growth in a loop

You will write the exponential and the logistic population, and find when a logistic population reaches half of its carrying capacity.

The idea. The exponential size is $N_0 e^{rt}$. The logistic size is $K / \left(1 + \dfrac{K - N_0}{N_0} e^{-rt}\right)$.

Your tasks.

1. Finish exponential. It gives the size after t years.
2. Finish logistic. It gives the logistic size after t years.
3. Finish years_to_half. It gives the first whole year in which the logistic size is at least $K/2$.