The rate (as a percentage) of $\mathrm{CO}_2$ contained in a room after $t$ minutes of hood operation is modelled by the function $f$ defined for all real $t$ in the interval $[0;20]$ by:
$$f(t) = (0{,}8t + 0{,}2)\mathrm{e}^{-0{,}5t} + 0{,}03.$$
In this question, round both results to the nearest thousandth.\\
a. Calculate $f(20)$.\\
b. Determine the maximum rate of $\mathrm{CO}_2$ present in the room during the experiment.