In a factory, a kiln bakes ceramics at a temperature of $1000^{\circ}\mathrm{C}$. At the end of baking, it is turned off and cools down. The temperature of the kiln is expressed in degrees Celsius (${}^{\circ}\mathrm{C}$). The kiln door can be opened safely for the ceramics as soon as its temperature is below $70^{\circ}\mathrm{C}$.

For a natural integer $n$, we denote $T_n$ the temperature in degrees Celsius of the kiln after $n$ hours have elapsed from the moment it was turned off. We therefore have $T_0 = 1000$. The temperature $T_n$ is calculated by the following algorithm:

\begin{verbatim}
T←1000
For i going from 1 to n
    T←0.82 x T+3.6
End For
\end{verbatim}

\begin{enumerate}
  \item Determine the temperature of the kiln, rounded to the nearest unit, after 4 hours of cooling.
  \item Prove that, for every natural integer $n$, we have: $T_n = 980 \times 0.82^n + 20$.
  \item After how many hours can the kiln be opened safely for the ceramics?
\end{enumerate}