To find the percentage of the pond that will be covered by the invasive water weed after 20 weeks, we need to evaluate the function \( A(t) = 3e^{0.15t} \) at \( t = 20 \).
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Plug \( t = 20 \) into the function: \[ A(20) = 3e^{0.15 \times 20} \] \[ A(20) = 3e^{3} \]
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Calculate \( e^{3} \) using a calculator (or by looking up the value): \[ e^{3} \approx 20.0855 \]
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Now, substitute back into the equation: \[ A(20) \approx 3 \times 20.0855 \approx 60.2565 \]
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Round this to the nearest whole number: \[ A(20) \approx 60 \text{ percent} \]
Therefore, the percentage of the pond that will be covered after 20 weeks is approximately 60 percent.