\[ 3 = e^{5k}. \]

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• Substitute into the equation:
• \[ 3P_0 = P_0 e^{5k}. \]
• Divide both sides by \( P_0 \):
• \[ \ln 3 = 5k. \]
• Solve for \( k \):
• \[ k = \frac{\ln 3}{5}. \]

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