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

Question

, 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

20 passengers
20 passengers

4 passengers
4 passengers

626,944 passengers
626,944 passengers

35 passengers

Answer 1

To find the number of infected passengers after one week (7 days), we can substitute \( t = 7 \) into the equation \( A(t) = 3e^{0.35t} \).

Calculating:

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

First, calculate \( 0.35 \cdot 7 \):

\[ 0.35 \cdot 7 = 2.45 \]

Now compute \( e^{2.45} \):

Using a calculator, we find:

\[ e^{2.45} \approx 11.605 \]

Now, substitute this value back into the equation:

\[ A(7) = 3 \cdot 11.605 \approx 34.815 \]

Rounding to the nearest whole number:

\[ A(7) \approx 35 \]

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