To find the percentage of the pond that will be covered after 20 weeks using the model \( A(t) = 3e^{0.15t} \), we'll substitute \( t = 20 \) into the equation.
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First, calculate \( e^{0.15 \times 20} \): \[ 0.15 \times 20 = 3 \] \[ e^3 \approx 20.0855 \quad (\text{using a calculator}) \]
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Now substitute this back into the equation: \[ A(20) = 3 \times e^3 \approx 3 \times 20.0855 \approx 60.2565 \]
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Rounding this to the nearest whole number gives us: \[ A(20) \approx 60 \text{ percent} \]
Thus, the percentage of the pond that will be covered after 20 weeks is approximately 60 percent.