To find the percentage of the pond covered by the invasive water weed after 20 weeks using the model \( A(t) = 3e^{0.15t} \), we can substitute \( t = 20 \) into the equation.
\[ A(20) = 3e^{0.15 \times 20} \]
Calculating \( 0.15 \times 20 \):
\[ 0.15 \times 20 = 3 \]
Now, substituting this back into the equation:
\[ A(20) = 3e^{3} \]
Next, we need to calculate \( e^{3} \). Using a calculator, \( e^{3} \approx 20.0855 \):
\[ A(20) = 3 \times 20.0855 \approx 60.2565 \]
Rounding to the nearest whole number:
\[ A(20) \approx 60 \]
Thus, the percentage of the pond that will be covered after 20 weeks is approximately 60%.