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Home » So only \(n \equiv 2 \pmod5\) works. - Upplift

So only \(n \equiv 2 \pmod5\) works. - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 P''(1) = 6(1) - 12 = -6 < 0 \Rightarrow \text{local maximum at } t = 1, \\

📌 P''(3) = 6(3) - 12 = 6 > 0 \Rightarrow \text{local minimum at } t = 3.

📌 Thus, the pressure reaches a local maximum at $ t = 1 $ hour (1:00 AM) and a local minimum at $ t = 3 $ hours (3:00 AM).

📌 \boxed{\text{Local maximum at } t = 1 \text{ hour, local minimum at } t = 3 \text{ hours}}

📌 Question: A zoologist observes that the number of daily interactions between two species in a reserve is modeled by the function $ I(t) = \frac{t^2 + 4}{t + 2} $, where $ t $ is time in days since the start of the study. Find the slant asymptote of $ I(t) $ as $ t \to \infty $.

📌 Solution: To find the slant asymptote of $ I(t) = \frac{t^2 + 4}{t + 2} $, we perform polynomial long division of $ t^2 + 4 $ by $ t + 2 $:

📌 Divide $ t^2 $ by $ t $ to get $ t $. Multiply $ t + 2 $ by $ t $ to get $ t^2 + 2t $. Subtract:

📌 Next, divide $ -2t $ by $ t $ to get $ -2 $. Multiply $ t + 2 $ by $ -2 $ to get $ -2t - 4 $. Subtract:

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