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Home » = 2^3, \quad 64 = 2^6 - Londonproperty

= 2^3, \quad 64 = 2^6 - Londonproperty

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 \(\boxed{b = -5, \, c = 6}\)

📌 An oceanographer studying the impacts of climate change is modeling the growth of algae blooms in a coastal region. The growth rate \( G(t) \) of the algae over time \( t \) is modeled by the function:

📌 \[ G(t) = \frac{3t^2 + 2t + 1}{t + 1} \]

📌 Find the horizontal asymptote of this function as \( t \to \infty \).

📌 To find the horizontal asymptote of the rational function \( G(t) = \frac{3t^2 + 2t + 1}{t + 1} \), we analyze the degrees of the numerator and the denominator.

📌 The degree of the numerator is 2, and the degree of the denominator is 1. Since the degree of the numerator is greater than the degree of the denominator, the function does not have a horizontal asymptote. Instead, it has an oblique (slant) asymptote.

📌 To find the slant asymptote, perform polynomial long division of \( 3t^2 + 2t + 1 \) by \( t + 1 \):

📌 Divide \( 3t^2 \) by \( t \) to get \( 3t \).

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