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The probability that at least one occurs is 0.58. - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 #### 432**Question:** A linguist is studying the evolution of language through a model where the frequency of a certain linguistic feature in a population is given by the function \( f(t) = 3t^2 - 2t + 5 \). Find the time \( t \) at which the frequency is 20.

📌 Solution:** To find the time \( t \) when the frequency \( f(t) = 20 \), we set up the equation:

📌 3t^2 - 2t + 5 = 20

📌 Subtract 20 from both sides:

📌 3t^2 - 2t + 5 - 20 = 0

📌 3t^2 - 2t - 15 = 0

📌 This is a quadratic equation in the form \( at^2 + bt + c = 0 \), where \( a = 3 \), \( b = -2 \), and \( c = -15 \). We use the quadratic formula:

📌 t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

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