The percentage of a pond that is covered by an invasive water weed after t weeks is modeled by A(t)=3e0.15t . To the nearest whole number, discover what percentage of the pond will be covered after 20 weeks.(1 point) Responses

1 answer

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%.