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Home » \[ 2 + 1.5 = 3.5 \, \texthours \] - Abu Waleed Tea

\[ 2 + 1.5 = 3.5 \, \texthours \] - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 oxed{rac{5 - \sqrt{7}}{9}}

📌 A pharmacologist is studying the concentration of a new Alzheimer's drug in the bloodstream, modeled by the function \( C(x) = 5x^2e^{-x} \). Determine the dosage level \( x \) that maximizes the concentration.

📌 To find the dosage level that maximizes the concentration, we first find the derivative of \( C(x) \):

📌 C'(x) = rac{d}{dx}(5x^2e^{-x}).

📌 Using the product rule, where \( u = 5x^2 \) and \( v = e^{-x} \), we have:

📌 C'(x) = u'v + uv' = (10x)e^{-x} + 5x^2(-e^{-x}) = e^{-x}(10x - 5x^2).

📌 Set \( C'(x) = 0 \) to find critical points:

📌 e^{-x}(10x - 5x^2) = 0.

🔥 Popular Posts

+ 0.05t = (1.04)^t
Solving numerically (logarithms or trial):
Try \( t = 8 \):
+ 0.05(8) = 1.4, \quad (1.04)^8 \approx 1.3686
Try \( t = 9 \):
+ 0.05(9) = 1.45, \quad (1.04)^9 \approx 1.4233
Try \( t = 10 \):
+ 0.05(10) = 1.5, \quad (1.04)^{10} \approx 1.4802
Try \( t = 11 \):
+ 0.55 = 1.55, \quad (1.04)^{11} \approx 1.5396

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