A culture that runs out of food

A flask starts with $500$ bacteria, and each divides every $30$ minutes, so the number is multiplied by $4$ every hour. But the flask can hold only $10^9$ cells. You will find the count at each hour, the first hour when the flask is full, and how many hours the culture keeps growing. Then the program draws the growth on a log scale.

The idea. Without a limit the count would be $500 \times 4^h$ after $h$ hours. The food runs out at the capacity, so the count can never pass it.

Your tasks.

1. Set counts to the number at each hour in hours, never more than capacity.
2. Set first_full to the first hour when the count equals capacity.
3. Set hours_growing to the number of hours in which the count went up from the hour before.