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)

Question

Responses

This is impossible to determine with the information provided.
This is impossible to determine with the information provided.

60 percent
60 percent

4 percent
4 percent

6,026 percent

Answer 1

To find the percentage of the pond covered by the invasive water weed after 20 weeks, we will evaluate the function \( A(t) = 3e^{0.15t} \) at \( t = 20 \).

First, we calculate \( A(20) \):

\[ A(20) = 3e^{0.15 \cdot 20} \]

Calculating the exponent:

\[ 0.15 \cdot 20 = 3 \]

Now substituting back in:

\[ A(20) = 3e^3 \]

Next, we compute \( e^3 \):

Using approximate value \( e \approx 2.718 \):

\[ e^3 \approx 2.718^3 \approx 20.0855 \]

Now we calculate:

\[ A(20) \approx 3 \cdot 20.0855 \approx 60.2565 \]

To the nearest whole number, this value is approximately:

\[ 60 \]

Thus, the percentage of the pond covered after 20 weeks is 60 percent.