Question
Euler's Number, e Quick Check
1 of 51 of 5 Items
Question
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
60 percent
60 percent
4 percent
4 percent
This is impossible to determine with the information provided.
This is impossible to determine with the information provided.
6,026 percent
6,026 percent
Skip to navigation
Answers
GPT-4o mini
To find the percentage of the pond that will be covered after 20 weeks using the model \( A(t) = 3e^{0.15t} \), we'll substitute \( t = 20 \) into the equation.
1. First, calculate \( e^{0.15 \times 20} \):
\[
0.15 \times 20 = 3
\]
\[
e^3 \approx 20.0855 \quad (\text{using a calculator})
\]
2. Now substitute this back into the equation:
\[
A(20) = 3 \times e^3 \approx 3 \times 20.0855 \approx 60.2565
\]
3. Rounding this to the nearest whole number gives us:
\[
A(20) \approx 60 \text{ percent}
\]
Thus, the percentage of the pond that will be covered after 20 weeks is approximately **60 percent**.
1. First, calculate \( e^{0.15 \times 20} \):
\[
0.15 \times 20 = 3
\]
\[
e^3 \approx 20.0855 \quad (\text{using a calculator})
\]
2. Now substitute this back into the equation:
\[
A(20) = 3 \times e^3 \approx 3 \times 20.0855 \approx 60.2565
\]
3. Rounding this to the nearest whole number gives us:
\[
A(20) \approx 60 \text{ percent}
\]
Thus, the percentage of the pond that will be covered after 20 weeks is approximately **60 percent**.