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Home » Only positive value: \( x = 2 + 2\sqrt5 \) - Portal da AcÃºstica

Only positive value: \( x = 2 + 2\sqrt5 \) - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 ThenQuestion: A plant biologist is studying a population of genetically modified wheat plants. The number of plants that survive after $ t $ weeks is modeled by the function $ S(t) = rac{t^2 + 5t + 6}{t + 2} $. What is the simplified expression for $ S(t) $, and what is the smallest integer value of $ t $ for which $ S(t) $ is an integer?

📌 We begin by simplifying the expression for $ S(t) $:

📌 S(t) = rac{t^2 + 5t + 6}{t + 2}

📌 t^2 + 5t + 6 = (t + 2)(t + 3)

📌 S(t) = rac{(t + 2)(t + 3)}{t + 2}

📌 eq -2 $, we can cancel $ t + 2 $:

📌 S(t) = t + 3

📌 Now, we are to find the smallest integer value of $ t $ such that $ S(t) $ is an integer. Since $ S(t) = t + 3 $ for all $ t

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