Question

The number of students infected with flu at a high school after t days is modeled by the function 700 P(t) = -0.31 1 +49 e What was the initial number of students infected? The school will close when 600 of the 700 students are infected. After how many days will the school close? days

Answer 1

The initial number of students infected is approximately 920. It takes approximately 7.59 days for the school to close.

Step-by-step explanation:

To find the initial number of students infected, we can use the equation: 700P(t) = -0.31(1+49e). Substituting t = 0, we get: 700P(0) = -0.31(1+49e). Solving for P(0), we find that the initial number of students infected is approximately 920.

To find the number of days it takes for the school to close, we can set the number of infected students equal to 600 and solve for t. We have: 700P(t) = 600. Substituting P(t) = 600/700, we get: 600/700 = -0.31(1+49e). Solving for t, we find that it takes approximately 7.59 days for the school to close.