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Check:
\[ S(4) = \frac{100}{16 + 1} = \frac{100}{17} \approx 5.882 > 5 \]
\[ S(5) = \frac{100}{25 + 1} = \frac{100}{26} \approx 3.846 < 5 \]
So, the sensitivity first drops below 5 at \(n = 5\).
\boxed{5}
A quantum sensor’s signal-to-noise ratio (SNR) is modeled by \( R(t) = 3t^2 - 12t + 15 \), where \(t\) is time in seconds. What is the minimum SNR achieved during operation?
The function \( R(t) = 3t^2 - 12t + 15 \) is a quadratic in standard form \( at^2 + bt + c \), with \( a = 3 > 0 \), so it opens upwards and has a minimum at its vertex.
The vertex occurs at:
t = -\frac{b}{2a} = -\frac{-12}{2 \cdot 3} = \frac{12}{6} = 2
Evaluate \( R(2) \):