Modélisation mathématique et surveillance numérique

Read the following excerpt: 'The boundary between fiction and reality is porous. In our digital age, the rate of surveillance grows according to the model $S(t) = S_0 \cdot e^{kt}$, where $S(t)$ represents the total volume of individual data points collected at time $t$ (in years), and $S_0$ is the initial observation volume. Every user generates a daily quota of $N$ data points. We are witnessing an exponential confinement where the cumulative data harvested is defined by the integral $$D = \int_{0}^{T} S(t) dt$.'

1. Analyze why the author uses the exponential model $S(t) = S_0 \cdot e^{kt}$ to describe the shift from personal privacy to data-driven surveillance.
2. Calculate the total data accumulation $D$ over a period $T$ and explain how the parameter $k$ influences the 'reality' of digital confinement compared to the static nature of fictional dystopias.