Question

An epidemiological study tracked the spread of a particular influenza strain in a small school population. The total number of students, P, who contracted the flu t days after the outbreak is modeled by P = - + 13t + 160, where t ranges from 1 to 6.

What is the day when 200 students had contracted the flu?

A) Day 3
B) Day 4
C) Day 5
D) Day 6

Answer 1

To determine the day when 200 students had contracted the flu, we solve the equation P = 13t + 160 by setting P to 200. This leads to t = 40 / 13, which is just above 3, indicating that Day 4 is the correct answer.

Step-by-step explanation:

The question pertains to finding the day on which the number of students who contracted the flu reached 200 in a small school population. The number of students, P, who contracted the flu t days after the outbreak is modeled by the equation P = 13t + 160. Since we need to find the day (t) when P is equal to 200, we can set up the equation 200 = 13t + 160 and solve for t.

To solve for t, we first subtract 160 from both sides of the equation, giving us:

40 = 13t

Next, we divide both sides by 13 to isolate t:

t = 40 / 13

This gives us approximately 3.08, which means that on Day 3, the number will be just over 200, and Day 4 is the first full day when the number of students with the flu exceeds 200. Thus, the correct answer is B) Day 4.