What does this equation mean?

Treated as a growth model rather than a guarantee, the trend can be written as $T(t) \;\approx\; T_0 \cdot 2^{\frac{t - t_0}{\tau}}, \qquad \tau \approx 7\ \text{months}$. where T(t) is the time-horizon at date t and $\tau$ is the empirical doubling period. This is a compact way to state a real, fitted regularity — it is not a physical law, and the paper’s own authors flag that the fit is over a specific task suite combining two internal benchmarks and a small set of newly written short tasks, not over arbitrary production software work, and that the entire extrapolation depends on whether that suite’s difficulty profile actually resembles the tasks an organization needs done. Reading a doubling constant off a fitted curve and projecting it five years forward is a scenario, not a fact; the fact is the fitted curve’s shape over the period actually measured.