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Home » Divide by 2 (the smallest prime number): - American Beagle Club

Divide by 2 (the smallest prime number): - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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So, the enclosed area is \( rac{8}{3} \) square units.
A population of bacteria doubles every 3 hours. If the initial populat...
Use exponential growth: \( P(t) = P_0 \cdot 2^{t/T} \), where \( T = 3...
\( P(12) = 500 \cdot 2^{12/3} = 500 \cdot 2^4 = 500 \cdot 16 = 8000 \)...
Thus, 8000 bacteria are present after 12 hours.
Solve the differential equation \( rac{dy}{dx} = 3y \) with initial c...
Separate variables: \( rac{dy}{y} = 3\,dx \).
Integrate both sides: \( \ln|y| = 3x + C \).
Exponentiate: \( y = e^{3x + C} = Ce^{3x} \).
Use \( y(0) = 2 \): \( 2 = Ce^0 \Rightarrow C = 2 \).

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