The antibody curve

You will write the model of the antibody level in the blood after a first and a second exposure, and use it to find the day of each peak.

The idea. The first response is $\dfrac{d}{12} e^{1 - d/12}$ on day $d$, with a peak of $1$ on day $12$. The second exposure adds a larger response that peaks $5$ days after it.

Your tasks.

1. Finish first_response. It gives the level day days after the first exposure.
2. Finish second_response. It gives the extra level that the second exposure adds. It is $0$ before the day gap. After that it is ratio times $\dfrac{s}{5} e^{1 - s/5}$, where $s$ is the days since the second exposure.
3. Finish peak_day. It gives the day with the highest level from start to end.