We are to find the smallest integer \(n\) such that:
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- So, the predicted temperature in 2100 with \(x = 250\) ppm is \(T(250) = 26.9055\), which rounds to approximately 26.9°C. However, since the question asks for the value predicted by the model at \(x = 250\), we report:
- \boxed{26.91}
- In quantum sensing, a researcher models the sensitivity of a sensor as \( S(n) = \frac{100}{n^2 + 1} \) when measuring at discrete time intervals \(n = 1, 2, 3, \ldots\) seconds. At what integer time \(n\) is the sensitivity first less than 5 units?
- S(n) = \frac{100}{n^2 + 1} < 5
- Solve the inequality:
- \frac{100}{n^2 + 1} < 5
