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Home » Hidden Secrets Inside the Needoh Advent Calendar—Click to Find Them Before Christmas! - Leaselab

Hidden Secrets Inside the Needoh Advent Calendar—Click to Find Them Before Christmas! - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 The leading coefficient of the numerator \( 3t^2 \) is 3, and of the denominator \( t^2 \) is 1. Thus, the horizontal asymptote is \( y = \frac{3}{1} = 3 \).

📌 Therefore, the horizontal asymptote is \(\boxed{y = 3}\).

📌 A zoologist observes that the population \( P \) of a certain species in the Amazon can be modeled by the equation \( P = \frac{500}{1 + e^{-0.1(t-5)}} \), where \( t \) is the number of months since the study began. Calculate the population of the species as \( t \) approaches infinity.

📌 To determine the population \( P \) as \( t \to \infty \), we analyze the behavior of the logistic function:

📌 \[ P = \frac{500}{1 + e^{-0.1(t-5)}} \]

📌 As \( t \to \infty \), the term \( e^{-0.1(t-5)} \to 0 \). Thus, the denominator approaches 1:

📌 \[ P \to \frac{500}{1 + 0} = 500 \]

📌 Therefore, the population approaches \(\boxed{500}\) as \( t \to \infty \).

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