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)ResponsesThis is impossible to determine with the information provided.This is impossible to determine with the information provided.60 percent60 percent4 percent4 percent6,026 percent

1 answer

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.