A biologist has modeled the evolution of a bacterial population (in thousands of entities) by the function $f$ defined on $[0; +\infty[$ by

$$f(t) = e^3 - e^{-0.5t^2 + t + 2}$$

where $t$ denotes the time in hours since the beginning of the experiment.\\
Based on this modeling, he proposes the three statements below.\\
For each of them, indicate, by justifying, whether it is true or false.

\begin{itemize}
  \item Statement 1: ``The population increases permanently''.
  \item Statement 2: ``In the long term, the population will exceed 21000 bacteria''.
  \item Statement 3: ``The bacterial population will have a count of 10000 on two occasions over time''.
\end{itemize}