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Home » The growth of the bacterial culture is exponential, doubling every hour. - Imagemakers

The growth of the bacterial culture is exponential, doubling every hour. - Imagemakers

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 A city planner is analyzing a model where the traffic flow \( f(t) \) through an intersection is given by the polynomial \( f(t) = 4t^3 - 9t^2 + 6t - 1 \). Compute the sum of the roots of the equation \( f(t) = 0 \).

📌 To find the sum of the roots of the polynomial \( f(t) = 4t^3 - 9t^2 + 6t - 1 \), we use Vieta's formulas. For a cubic equation \( at^3 + bt^2 + ct + d = 0 \), the sum of the roots is given by \( -\frac{b}{a} \).

📌 Here, \( a = 4 \) and \( b = -9 \). Therefore, the sum of the roots is:

📌 -\frac{-9}{4} = \frac{9}{4}

📌 Thus, the sum of the roots is \(\boxed{\frac{9}{4}}\).

📌 A science communicator is explaining the exponential growth of bacteria in a petri dish. If the growth is modeled by the equation \( 5e^{kt} = 100 \), where \( k \) and \( t \) are positive, solve for \( t \) when \( k = 0.3 \).

📌 Start by isolating the exponential term:

📌 e^{0.3t} = \frac{100}{5} = 20

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