Question

After the outbreak of a contagious virus on a cruise ship, epidemiologists find that the number of infected passengers is represented by A(t)=3e0.35t
, where t represents the number of days since the first diagnosis. How many passengers will be infected after one week? Round your answer to the nearest whole number.(1 point)
Responses

626,944 passengers
626,944 passengers

20 passengers
20 passengers

35 passengers
35 passengers

4 passengers

Answer 1

To find the number of infected passengers after one week (7 days), we need to evaluate the function \( A(t) = 3e^{0.35t} \) at \( t = 7 \).

Substituting \( t = 7 \):

\[
A(7) = 3e^{0.35 \times 7}
\]
\[
A(7) = 3e^{2.45}
\]

Now, we calculate \( e^{2.45} \):

Using a calculator, you find that:

\[
e^{2.45} \approx 11.6
\]

Now substitute this value back into the equation:

\[
A(7) \approx 3 \times 11.6 \approx 34.8
\]

Rounding to the nearest whole number, we find:

\[
A(7) \approx 35
\]

Thus, the number of passengers infected after one week is approximately **35 passengers**.