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Home » \( 25\% \times 8 \text minutes = 0.25 \times 8 = 2 \text minutes \) - 500apps

\( 25\% \times 8 \text minutes = 0.25 \times 8 = 2 \text minutes \) - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📝 Recent Posts

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 \( y(0) = 2 \): \( 2 = Ce^0 \Rightarrow C = 2 \).
So, \( y = 2e^{3x} \).

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