To determine the percentage of the pond that is covered by the invasive water weed after 20 weeks using the model \( A(t) = 3e^{0.15t} \), we will substitute \( t = 20 \) into the equation.
The calculation is as follows:
\[ A(20) = 3e^{0.15 \times 20} \]
First, calculate \( 0.15 \times 20 \):
\[ 0.15 \times 20 = 3 \]
Now substitute that back into the equation:
\[ A(20) = 3e^{3} \]
Next, we need to calculate \( e^{3} \). The value of \( e \) (approximately 2.71828) raised to the power of 3 is approximately equal to:
\[ e^{3} \approx 20.0855 \]
Now, we can calculate \( A(20) \):
\[ A(20) \approx 3 \times 20.0855 \approx 60.2565 \]
Rounding to the nearest whole number gives us:
\[ A(20) \approx 60 \]
Thus, the percentage of the pond that will be covered after 20 weeks is approximately 60 percent.
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