Question

7. suppose a student carrying a flu virus returns to an isolated college campus of 1000 students. determine a differential equation for the number of people x(t) who have contracted the flu if the rate at which the disease spreads is proportional to the number of interactions between the number of students who have the flu and the number of students who have not yet been exposed to it. (Use k > 0 for the constant of proportionality and x for x(t).)

Answer 1

Answer: If the rate at which the flu spreads is proportional to the number of interactions between students who have the flu and students who have not been exposed to it, we can write:

dx/dt = kx(1000 - x)

where x is the number of students who have contracted the flu, k is the constant of proportionality, and t is time. The term x(1000 - x) represents the number of interactions between the students who have the flu and the students who have not been exposed to it. The factor of 1000 - x represents the number of students who have not yet been exposed to the flu.

Thus, the differential equation models the spread of the flu on the isolated college campus as the number of people who have contracted the flu changes over time due to the number of interactions between the students who have the flu and the students who have not been exposed to it.

Explanation: