We want the smallest integer \(t\) such that:
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- Using quantum sensing in ecological monitoring, a scientist finds that the growth rate of a rare plant species under controlled stress is modeled by \( P(t) = 2e^{0.3t} \), where \(t\) is time in days. After how many full days will the population first exceed 20 times its initial size?
- Initial population at \(t = 0\):
- \[ P(0) = 2e^{0} = 2 \]
- \[ P(t) > 20 \times 2 = 40 \]
- 2e^{0.3t} > 40
- Divide both sides by 2:
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