Final answer:
The initial number of students infected with the flu was 300, as indicated by evaluating N(0). After 3 days, by evaluating N(3) and using e^0.33 ≈ 1.391, the model predicts that approximately 417 students would be infected.
Step-by-step explanation:
The student's question involves the mathematical modeling of an infectious disease spread within a school over time using the exponential growth function. Specifically, they are using the function N(t) = 300 * e^0.11t to model the number of students infected with the flu at Dragonstone High School t days after exposure.
(a) Initial number of students infected with the flu:
To find the initial number of students infected, we need to evaluate N(0), since t represents the number of days after exposure, and at t=0, it would be the initial count.
N(0) = 300 * e^0.11*0 = 300 * e^0 = 300 * 1 = 300
So, the initial number of students infected was 300.
(b) Number of students infected after 3 days:
To find how many students were infected after 3 days, we evaluate N(3):
N(3) = 300 * e^0.11*3
First, let's calculate e^0.11*3.
e^(0.11*3) is approximately e^0.33.
Using a calculator, we find that e^0.33 is approximately 1.391.
Now we multiply this result by 300:
300 * 1.391 = 417.3
Therefore, approximately 417 students would be infected after 3 days, considering that N(t) must be an integer because you can't have a fraction of a person infected.